Exam 11: Equilibrium and Elasticity

Mass on a spring: An object that weighs 2.450 N is attached to an ideal massless spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the spring constant of the spring?

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

Simple harmonic motion: 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.)

Energy in SHM: 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.

Simple harmonic motion: 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?

Simple harmonic motion: A machine part is vibrating along the x-axis in simple harmonic motion with a period of 0.27 s and a range (from the maximum in one direction to the maximum in the other) of 3.0 cm. At time t = 0 it is at its central position and moving in the +x direction. What is its position when t = 55 s?

Mass on a spring: A 1.6-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 190 N/m. The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. What is the velocity of the block at time t = 0.40 s?

Damped harmonic motion: A 2.15 kg lightly damped harmonic oscillator has an angular oscillation frequency of 0.261 rad/s. If the maximum displacement of occurs when t = 0.00 s, and the damping constant b is 0.74 kg/s what is the object's displacement when t = 4.01 s?

Simple pendulum: A frictionless pendulum clock on the surface of the earth has a period of 1.00 s. On a distant planet, the length of the pendulum must be shortened slightly to have a period of 1.00 s. What is true about the acceleration due to gravity on the distant planet?

Simple harmonic motion: A simple harmonic oscillator has an amplitude of 3.50 cm and a maximum speed of 26.0 cm/s. What is its speed when the displacement is 1.75 cm?

Simple pendulum: A certain frictionless simple pendulum having a length L and mass M swings with period T. If both L and M are doubled, what is the new period?

Physical pendulum: 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?

Energy in SHM: An object of mass 6.8 kg is attached to an ideal massless spring of spring constant 1690 N/m. The object is pulled from its equilibrium position at x = 0.00 m to a displacement x = 0.35 m and is released from rest. Calculate the maximum speed the object reaches during its motion.

Mass on a spring: An object of mass 8.0 kg is attached to an ideal massless spring and allowed to hang in the Earth's gravitational field. The spring stretches 3.6 cm before it reaches its equilibrium position. If this system is allowed to oscillate, what will be its frequency?

Physical pendulum: A large stick is pivoted about one end and allowed to swing back and forth with no friction as a physical pendulum. The mass of the stick is and its center of gravity (found by finding its balance point) is from the pivot. If the period of the swinging stick is what is the moment of inertia of the stick about an axis through the pivot?

Damped harmonic motion: A lightly damped harmonic oscillator, with a damping force proportional to its speed, is oscillating with an amplitude of 0.500 cm at time t = 0. When t = 8.20 s, the amplitude has died down to 0.400 cm. At what value of t will the oscillations have an amplitude of 0.250 cm?

Simple harmonic motion: 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?

Physical pendulum: A long thin uniform rod of length 1.50 m is to be suspended from a frictionless pivot located at some point along the rod so that its pendulum motion takes 3.00 s. How far from the center of the rod should the pivot be located?

Damped harmonic motion: 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?

Simple harmonic motion: An object is undergoing simple harmonic motion with frequency f = 9.7 Hz and an amplitude of 0.12 m. At t = 0.00 s the object is at x = 0.00 m. How long does it take the object to go from .00 m to