Exam 15: Oscillations

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. (a)What is the maximum speed of the needle? (b)What is the maximum acceleration of the needle?

Which of following graphs describes simple periodic motion with amplitude 2.00 cm and angular frequency 2.00 rad/s?

A 25 kg object is undergoing lightly damped harmonic oscillations.If the maximum displacement of the object from its equilibrium point drops to 1/3 its original value in 1.8 s,what is the value of the damping constant b?

A 5.0-kg block is attached to an ideal massless spring whose spring constant is 125 N/m.The block is pulled from its equilibrium position at x = 0.00 m to a position at x = +0.687 m and is released from rest.The block then executes lightly damped oscillation along the x-axis,and the damping force is proportional to the velocity.When the block first returns to x = 0.00 m,its x component of velocity is -2.0 m/s and its x component of acceleration is +5.6 m/s². (a)What is the magnitude of the acceleration of the block upon release at x = +0.687 m. (b)Find the damping constant b.

A uniform meter stick is freely pivoted about the 0.20-m mark.If it is allowed to swing in a vertical plane with a small amplitude and friction,what is the frequency of its oscillations?

In the figure,a 0.24-kg ball is suspended from a very light string 9.79 m long and is pulled slightly to the left.As the ball swings without friction through the lowest part of its motion it encounters an ideal massless spring attached to the wall.The spring pushes against the ball and eventually the ball is returned to its original starting position.Find the time for one complete cycle of this motion if the spring constant of the spring is 21 N/m.(Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball.)

In simple harmonic motion,the speed is greatest at that point in the cycle when

A mass M is attached to an ideal massless spring.When this system is set in motion,it has a period T.What is the period if the mass is doubled to 2M?

A 1.5-kg mass attached to an ideal massless spring with a spring constant of 20.0 N/m oscillates on a horizontal,frictionless track.At time t = 0.00 s,the mass is released from rest at x = 10.0 cm.(That is,the spring is stretched by 10.0 cm.) (a)Find the frequency of the oscillations. (b)Determine the maximum speed of the mass.At what point in the motion does the maximum speed occur? (c)What is the maximum acceleration of the mass? At what point in the motion does the maximum acceleration occur? (d)Determine the total energy of the oscillating system. (e)Express the displacement x as a function of time t.

If we double only the spring constant of a vibrating ideal mass-and-spring system,the mechanical energy of the system

The x component of the velocity of an object vibrating along the x-axis obeys the equation v_x(t)= (0.445 m/s)sin[(25.4 rad/s)t + 0.223]. (a)What is the amplitude of the motion of this object? (b)What is the maximum acceleration of the vibrating object?

A 2.0 kg block on a frictionless table is connected to two ideal massless springs with spring constants k₁ and k₂ whose opposite ends are fixed to walls,as shown in the figure.What is angular frequency of the oscillation if and

In designing buildings to be erected in an area prone to earthquakes,what relationship should the designer try to achieve between the natural frequency of the building and the typical earthquake frequencies?

A 0.25 kg ideal harmonic oscillator has a total mechanical energy of If the oscillation amplitude is what is the oscillation frequency?

The position x of an object varies with time t.For which of the following equations relating x and t is the motion of the object simple harmonic motion? (There may be more than one correct choice.) A)x = 5 sin²3t B)x = 8 cos 3t C)x = 4 tan 2t D)x = 5 sin 3t E)x = 2 cos(3t - 1)

The simple harmonic motion of an object is described by the graph shown in the figure.What is the equation for the position x(t)of the object as a function of time t?

A restoring force of magnitude F acts on a system with a displacement of magnitude x.In which of the following cases will the system undergo simple harmonic motion?

An object weighing 44.1 N hangs from a vertical massless ideal spring.When set in vertical motion,the object obeys the equation y(t)= (6.20 cm)cos[(2.74 rad/s)t - 1.40]. (a)Find the time for this object to vibrate one complete cycle. (b)What are the maximum speed and maximum acceleration of the object. (c)What is the TOTAL distance the object moves through in one cycle. (d)Find the maximum kinetic energy of the object. (e)What is the spring constant of the spring.

A 12.0-N object is oscillating in simple harmonic motion at the end of an ideal vertical spring.Its vertical position y as a function of time t is given by y(t)= 4.50 cm cos[(19.5 s^-1)t - π/8]. (a)What is the spring constant of the spring? (b)What is the maximum acceleration of the object? (c)What is the maximum speed that the object reaches? (d)How long does it take the object to go from its highest point to its lowest point?

The amplitude of a lightly damped harmonic oscillator decreases from 60.0 cm to 40.0 cm in 10.0 s.What will be the amplitude of the harmonic oscillator after another 10.0 s passes?