Question 1

The amplitude of a system moving with simple harmonic motion is doubled.The total energy will then be

Accepted Answer

A) 4 times as large 
B) 3 times as large 
C) 2 times as large 
D) the same as it was 
E) half as much 
A) 4 times as large 
B) 3 times as large 
C) 2 times as large 
D) the same as it was 
E) half as much A

Question 2

A hoop,a solid cylinder,and a solid sphere all have the same mass m and the same radius R.Each is mounted to oscillate about an axis a distance 0.5 R from the center.The axis is perpendicular to the circular plane of the hoop and the cylinder and to an equatorial plane of the sphere as shown below.Which is the correct ranking in order of increasing angular frequency ω?

Accepted Answer

A) hoop,cylinder,sphere 
B) cylinder,sphere,hoop 
C) sphere,cylinder,hoop 
D) hoop,sphere,cylinder 
E) sphere,hoop,cylinder 
A) hoop,cylinder,sphere 
B) cylinder,sphere,hoop 
C) sphere,cylinder,hoop 
D) hoop,sphere,cylinder 
E) sphere,hoop,cylinder A

Question 3

Exhibit 15-1
A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below.A point or points at which the object has positive velocity and zero acceleration is(are)   Use this exhibit to answer the following question(s).
-Refer to Exhibit 15-1.The point at which the object has zero velocity and negative acceleration is

Accepted Answer

A) A 
B) B 
C) C 
D) D 
E) E 
A) A 
B) B 
C) C 
D) D 
E) E B

Question 4

Exhibit 15-1
A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below.A point or points at which the object has positive velocity and zero acceleration is(are)   Use this exhibit to answer the following question(s).
-Refer to Exhibit 15-1.The point at which the object has negative velocity and zero acceleration is

Accepted Answer

A) A 
B) B 
C) C 
D) D 
E) E 
A) A 
B) B 
C) C 
D) D 
E) E

Question 5

A horizontal plank (m = 2.0 kg,L = 1.0 m)is pivoted at one end.A spring (k = 1.0 × 103 N/m)is attached at the other end,as shown in the figure.Find the angular frequency (in rad/s)for small oscillations.

Accepted Answer

A) 39 
B) 44 
C) 55 
D) 66 
E) 25 
A) 39 
B) 44 
C) 55 
D) 66 
E) 25

Question 6

A 2.00 m-long 6.00 kg ladder pivoted at the top hangs down from a platform at the circus.A 42.0 kg trapeze artist climbs to a point where her center of mass is at the center of the ladder and swings at the system's natural frequency.The angular frequency (in s−1)of the system of ladder and woman is

Accepted Answer

A) 1.01. 
B) 3.07. 
C) 4.03. 
D) 8.05. 
E) 16.2. 
A) 1.01. 
B) 3.07. 
C) 4.03. 
D) 8.05. 
E) 16.2.

Question 7

An automobile (m = 1.00 × 103 kg)is driven into a brick wall in a safety test.The bumper behaves like a spring (k = 5.00 × 106 N/m),and is observed to compress a distance of 3.16 cm as the car is brought to rest.What was the initial speed of the automobile?

Accepted Answer

Question 8

A damped oscillator is released from rest with an initial displacement of 10.00 cm.At the end of the first complete oscillation the displacement reaches 9.05 cm.When 4 more oscillations are completed,what is the displacement reached?

Accepted Answer

A) 7.41 cm 
B) 6.71 cm 
C) 6.07 cm 
D) 5.49 cm 
E) 5.25 cm 
A) 7.41 cm 
B) 6.71 cm 
C) 6.07 cm 
D) 5.49 cm 
E) 5.25 cm

Question 9

A body oscillates with simple harmonic motion along the x axis.Its displacement varies with time according to the equation x = 5.0 cos (πt).The magnitude of the acceleration (in m/s2)of the body at t = 1.0 s is approximately

Accepted Answer

A) 3.5 
B) 49 
C) 14 
D) 43 
E) 4.3 
A) 3.5 
B) 49 
C) 14 
D) 43 
E) 4.3

Question 10

Two circus clowns (each having a mass of 50 kg)swing on two flying trapezes (negligible mass,length 25 m)shown in the figure.At the peak of the swing,one grabs the other,and the two swing back to one platform.The time for the forward and return motion is

Accepted Answer

A) 10 s 
B) 50 s 
C) 15 s 
D) 20 s 
E) 25 s 
A) 10 s 
B) 50 s 
C) 15 s 
D) 20 s 
E) 25 s

Question 11

The motion of a particle connected to a spring is described by x = 10 sin (πt).At what time (in s)is the potential energy equal to the kinetic energy?

Accepted Answer

A) 0 
B) 0.25 
C) 0.50 
D) 0.79 
E) 1.0 
A) 0 
B) 0.25 
C) 0.50 
D) 0.79 
E) 1.0

Question 12

A uniform rod (mass m = 1.0 kg and length L = 2.0 m)pivoted at one end oscillates in a vertical plane as shown below.The period of oscillation (in s)is approximately

Accepted Answer

A) 4.0 
B) 1.6 
C) 3.2 
D) 2.3 
E) 2.0 
A) 4.0 
B) 1.6 
C) 3.2 
D) 2.3 
E) 2.0

Question 13

Ellen says that whenever the acceleration is directly proportional to the displacement of an object from its equilibrium position,the motion of the object is simple harmonic motion.Mary says this is true only if the acceleration is opposite in direction to the displacement.Which one,if either,is correct?

Accepted Answer

A) Ellen,because ω2 is directly proportional to the constant multiplying the displacement and to the mass. 
B) Ellen,because ω2 is directly proportional to the mass. 
C) Mary,because ω2 is directly proportional to the constant multiplying the displacement and to the mass. 
D) Mary,because ω2 is directly proportional to the mass. 
E) Mary,because the second derivative of an oscillatory function like sin(ωt)or cos(ωt)is always proportional to the negative of the original function. 
A) Ellen,because ω2 is directly proportional to the constant multiplying the displacement and to the mass. 
B) Ellen,because ω2 is directly proportional to the mass. 
C) Mary,because ω2 is directly proportional to the constant multiplying the displacement and to the mass. 
D) Mary,because ω2 is directly proportional to the mass. 
E) Mary,because the second derivative of an oscillatory function like sin(ωt)or cos(ωt)is always proportional to the negative of the original function.

Question 14

When a damping force is applied to a simple harmonic oscillator which has period T0 in the absence of damping,the new period T is such that

Accepted Answer

A) T 0. 
B) T = T0. 
C) T > T0. 
D) ωT 0T0. 
E) ωT > ω0T0. 
A) T 0. 
B) T = T0. 
C) T > T0. 
D) ωT 0T0. 
E) ωT > ω0T0.

Question 15

John says that the value of the function cos[ω(t + T)+ ϕ],obtained one period T after time t,is greater than cos(ωt + ϕ)by 2π.Larry says that it is greater by the addition of 1.00 to cos(ωt + ϕ).Which one,if either,is correct?

Accepted Answer

A) John,because ωT = 2π. 
B) John,because ωT = 1 radian. 
C) Larry,because ωT = 2π. 
D) Larry,because ωT = 1 radian. 
E) Neither,because cos(θ + 2π)= cosθ. 
A) John,because ωT = 2π. 
B) John,because ωT = 1 radian. 
C) Larry,because ωT = 2π. 
D) Larry,because ωT = 1 radian. 
E) Neither,because cos(θ + 2π)= cosθ.

Question 16

Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles θ1,θ2 and θ3 respectively and released.The approximation sin θ = θ holds for all three angles,with θ3 > θ2 > θ1.How do the angular frequencies of the three pendulums compare?

Accepted Answer

A) ω3 > ω2 > ω1 
B) Need to know amplitudes to answer this question. 
C) Need to know   to answer this question. 
D) ω1 > ω2 > ω3 
E) ω1 = ω2 = ω3 
A) ω3 > ω2 > ω1 
B) Need to know amplitudes to answer this question. 
C) Need to know   to answer this question. 
D) ω1 > ω2 > ω3 
E) ω1 = ω2 = ω3

Question 17

The motion of a piston in an auto engine is simple harmonic.If the piston travels back and forth over a distance of 10 cm,and the piston has a mass of 1.5 kg,what is the maximum speed of the piston and the maximum force acting on the piston when the engine is running at 4 200 rpm?

Accepted Answer

The answer of The motion of a piston in an...

Question 18

In an inertia balance,a body supported against gravity executes simple harmonic oscillations in a horizontal plane under the action of a set of springs.If a 1.00 kg body vibrates at 1.00 Hz,a 2.00 kg body will vibrate at

Accepted Answer

A) 0.500 Hz. 
B) 0.707 Hz. 
C) 1.00 Hz. 
D) 1.41 Hz. 
E) 2.00 Hz. 
A) 0.500 Hz. 
B) 0.707 Hz. 
C) 1.00 Hz. 
D) 1.41 Hz. 
E) 2.00 Hz.

Question 19

A body of mass 5.0 kg is suspended by a spring which stretches 10 cm when the mass is attached.It is then displaced downward an additional 5.0 cm and released.Its position as a function of time is approximately

Accepted Answer

A) y = −0.10 sin 9.9t 
B) y = 0.10 cos 9.9t 
C) y = −0.10 cos (9.9t + .1) 
D) y = 0.10 sin (9.9t + 5) 
E) y = −0.05 cos 9.9t 
A) y = −0.10 sin 9.9t 
B) y = 0.10 cos 9.9t 
C) y = −0.10 cos (9.9t + .1) 
D) y = 0.10 sin (9.9t + 5) 
E) y = −0.05 cos 9.9t

Question 20

The mass in the figure slides on a frictionless surface.If m = 2 kg,k1 = 800 N/m and k2 = 500 N/m,the frequency of oscillation (in Hz)is approximately

Accepted Answer

A) 6 
B) 2 
C) 4 
D) 8 
E) 10 
A) 6 
B) 2 
C) 4 
D) 8 
E) 10

Exam 15: Oscillatory Motion

The amplitude of a system moving with simple harmonic motion is doubled.The total energy will then be

A horizontal plank (m = 2.0 kg,L = 1.0 m)is pivoted at one end.A spring (k = 1.0 × 103 N/m)is attached at the other end,as shown in the figure.Find the angular frequency (in rad/s)for small oscillations.

An automobile (m = 1.00 × 103 kg)is driven into a brick wall in a safety test.The bumper behaves like a spring (k = 5.00 × 106 N/m),and is observed to compress a distance of 3.16 cm as the car is brought to rest.What was the initial speed of the automobile?

A damped oscillator is released from rest with an initial displacement of 10.00 cm.At the end of the first complete oscillation the displacement reaches 9.05 cm.When 4 more oscillations are completed,what is the displacement reached?

A body oscillates with simple harmonic motion along the x axis.Its displacement varies with time according to the equation x = 5.0 cos (πt).The magnitude of the acceleration (in m/s2)of the body at t = 1.0 s is approximately

Two circus clowns (each having a mass of 50 kg)swing on two flying trapezes (negligible mass,length 25 m)shown in the figure.At the peak of the swing,one grabs the other,and the two swing back to one platform.The time for the forward and return motion is

The motion of a particle connected to a spring is described by x = 10 sin (πt).At what time (in s)is the potential energy equal to the kinetic energy?

A uniform rod (mass m = 1.0 kg and length L = 2.0 m)pivoted at one end oscillates in a vertical plane as shown below.The period of oscillation (in s)is approximately

When a damping force is applied to a simple harmonic oscillator which has period T0 in the absence of damping,the new period T is such that

John says that the value of the function cos[ω(t + T)+ ϕ],obtained one period T after time t,is greater than cos(ωt + ϕ)by 2π.Larry says that it is greater by the addition of 1.00 to cos(ωt + ϕ).Which one,if either,is correct?

Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles θ1,θ2 and θ3 respectively and released.The approximation sin θ = θ holds for all three angles,with θ3 > θ2 > θ1.How do the angular frequencies of the three pendulums compare?

The motion of a piston in an auto engine is simple harmonic.If the piston travels back and forth over a distance of 10 cm,and the piston has a mass of 1.5 kg,what is the maximum speed of the piston and the maximum force acting on the piston when the engine is running at 4 200 rpm?

In an inertia balance,a body supported against gravity executes simple harmonic oscillations in a horizontal plane under the action of a set of springs.If a 1.00 kg body vibrates at 1.00 Hz,a 2.00 kg body will vibrate at

A body of mass 5.0 kg is suspended by a spring which stretches 10 cm when the mass is attached.It is then displaced downward an additional 5.0 cm and released.Its position as a function of time is approximately

The mass in the figure slides on a frictionless surface.If m = 2 kg,k1 = 800 N/m and k2 = 500 N/m,the frequency of oscillation (in Hz)is approximately

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A horizontal plank (m = 2.0 kg,L = 1.0 m)is pivoted at one end.A spring (k = 1.0 × 10³ N/m)is attached at the other end,as shown in the figure.Find the angular frequency (in rad/s)for small oscillations.

An automobile (m = 1.00 × 10³ kg)is driven into a brick wall in a safety test.The bumper behaves like a spring (k = 5.00 × 10⁶ N/m),and is observed to compress a distance of 3.16 cm as the car is brought to rest.What was the initial speed of the automobile?

A body oscillates with simple harmonic motion along the x axis.Its displacement varies with time according to the equation x = 5.0 cos (πt).The magnitude of the acceleration (in m/s²)of the body at t = 1.0 s is approximately

When a damping force is applied to a simple harmonic oscillator which has period T₀ in the absence of damping,the new period T is such that

Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles θ₁,θ₂ and θ₃ respectively and released.The approximation sin θ = θ holds for all three angles,with θ₃ > θ₂ > θ₁.How do the angular frequencies of the three pendulums compare?

The mass in the figure slides on a frictionless surface.If m = 2 kg,k₁ = 800 N/m and k₂ = 500 N/m,the frequency of oscillation (in Hz)is approximately