Question

A mass of 100 g stretches a spring 5 cm. If the mass is set in...

A mass of 100 g stretches a spring 5 cm. If the mass is set in motion from its equilibrium position with a downward velocity of 10 cm/s, and if there is no damping, determine the position u of the mass at any time t. (Use g = 9.8 m/s2  for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds.)

u(t) =

When does the mass first return to its equilibrium position?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A mass of 50 g stretches a spring 1.568 cm. If the mass is set in...
A mass of 50 g stretches a spring 1.568 cm. If the mass is set in motion from its equilibrium position with a downward velocity of 40 cm/s, and if there is no damping, determine the position u of the mass at any time t. Enclose arguments of functions in parentheses. For example, sin(2x). Assume g=9.8 ms2. Enter an exact answer. u(t)=?
A mass of 100 g stretches a spring 1.568 cm. If the mass is set in...
A mass of 100 g stretches a spring 1.568 cm. If the mass is set in motion from its equilibrium position with a downward velocity of 40 cms, and if there is no damping, determine the position u of the mass at any time t. Enclose arguments of functions in parentheses. For example, sin(2x).
A mass of 3 kg stretches a spring 61.25 cm. Supposing that there is no damping...
A mass of 3 kg stretches a spring 61.25 cm. Supposing that there is no damping and that the mass is set in motion from 0.5 m above its equilibrium position with a downward velocity of 2 m/s, determine the position of the mass at any time. Find the amplitude, the frequency, the period and the phase shift of the motion.
A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to...
A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to 2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 9 ft/s. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(t) = Find the time at which the mass attains its...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released from rest from a point 3 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1 2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released from rest from a point 3 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1 2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 10 cos(3t). (Use g = 32 ft/s2 for the acceleration...
A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to...
A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to sqrt(2) times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 9 ft/s. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(t) = Find the time at which the mass attains its...
A mass weighing 3 lb stretches a spring 3 in. If the mass is pushed upward,...
A mass weighing 3 lb stretches a spring 3 in. If the mass is pushed upward, contracting the spring a distance of 1 in, and then set in motion with a downward velocity of 2 ft/s, and if there is no damping, find the position u of the mass at any time t. Determine the frequency, period, amplitude, and phase of the motion
A force of 400N stretches a string 2 meters. A mass of 50kg is attached to...
A force of 400N stretches a string 2 meters. A mass of 50kg is attached to the end of the spring and stretches the spring to a length of 4 meters. The medium the spring passes through creates a damping force numerically equal to half the instantaneous velocity. If the spring is initially released from equilibrium with upward velocity of 10 m/s. a) Find the equation of motion. b) Find the time at which the mass attains its extreme displacement...
A mass of 1 kg stretches a spring 9.8 m. The mass is acted on by...
A mass of 1 kg stretches a spring 9.8 m. The mass is acted on by an external force of 4 cos(t) N. If the mass is set in motion from its equilibrium position with a downward velocity of 2 m/s, find the position of the mass at any time. Identify the transient (i.e., complementary) and steady state (i.e., particular) solutions. Does the motion exhibit resonance or a beat?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT