Exam 15: Periodic Motion

An ideal massless spring with a spring constant of 2.00 N/m is attached to an object of 75.0 g.The system has a small amount of damping.If the amplitude of the oscillations decreases from 10.0 mm to 5.00 mm in 15.0 s,what is the magnitude of the damping constant b?

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 5.40 kg and its center of gravity (found by finding its balance point)is 1.80 m from the pivot.If the period of the swinging stick is 6.90 seconds,what is the moment of inertia of the stick about an axis through the pivot?

A 0.28-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 500 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.When the displacement is x = -0.052 m,find the acceleration of the block.

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 x = 0.00 m to x = 0.048 m?

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 56.0 kg bungee jumper jumps off a bridge and undergoes simple harmonic motion.If the period of oscillation is 11.2 s,what is the spring constant of the bungee cord,assuming it has negligible mass compared to that of the jumper?

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

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?

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

A 0.025-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 150 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.When the displacement is x = 0.024 m,what is the kinetic energy of the block?

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 k₁ = 7.6 N/m and k₂ = 5.0 N/m?

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

An object of mass 6.8 kg is attached to an ideal massless spring of spring constant 1690 N/m.The object is Calculate the maximum speed the object reaches during its motion.

The angle that a swinging simple pendulum makes with the vertical obeys the equation Θ(t)= (0.150 rad)cos[(2.85 rad/s)t + 1.66]. (a)What is the length of the pendulum? A)0.15 m B)0.83 m C)1.21 m D)2.02 m E)It cannot be determined from the information given. (b)What is the mass of the swinging bob at the end of the pendulum? A)2.85 kg B)1.66 kg C)0.454 kg D)0.150 kg E)It cannot be determined from the information given.

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

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?

A 0.50-kg object is attached to an ideal massless spring of spring constant 20 N/m along a horizontal,frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. (a)What is the amplitude of vibration? (b)At what location are the kinetic energy and the potential energy of the system the same?

A frictionless pendulum released from 65 degrees with the vertical will vibrate with the same frequency as if it were released from 5 degrees with the vertical because the period is independent of the amplitude and mass.

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?

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.