Exam 15: Periodic Motion

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 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?

A 0.25 kg ideal harmonic oscillator has a total mechanical energy of 4.0 J.If the oscillation amplitude is 20.0 cm,what is the oscillation frequency?

A 2.15 kg lightly damped harmonic oscillator has an angular oscillation frequency of 0.261 rad/s.If the maximum displacement of 2.0 m 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?

A 2.00-kg object is attached to an ideal massless horizontal spring of spring constant 100.0 N/m and is at rest on a frictionless horizontal table.The spring is aligned along the x-axis and is fixed to a peg in the table.Suddenly this mass is struck by another 2.00-kg object traveling along the x-axis at 3.00 m/s,and the two masses stick together.What are the amplitude and period of the oscillations that result from this collision?

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?

An object is attached to a vertical ideal massless spring and bobs up and down between the two extreme points A and B.When the kinetic energy of the object is a minimum,the object is located

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?

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?

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 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?

The position of an object that is oscillating on an ideal spring is given by the equation x = (12.3 cm)cos[(1.26s^-1)t].At time t = 0.815 s, (a)how fast is the object moving? (b)what is the magnitude of the acceleration of the object?

An object is executing simple harmonic motion.What is true about the acceleration of this object? (There may be more than one correct choice.)

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?

A 2.25-kg object is attached to a horizontal an ideal massless spring on a frictionless table.What should be the spring constant of this spring so that the maximum acceleration of the object will be g when it oscillates with amplitude of 4.50 cm?

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.

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 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?

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?

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