A 2.5kg object oscillates at the end of a vertically hanging light spring once every 0.65s...

A 2.5kg object oscillates at the end of a vertically hanging light spring once every 0.65s .

Part A

Write down the equation giving its position y (+ upward) as a function of time t. Assume the object started by being compressed 17cm from the equilibrium position (where y = 0), and released.

Write down the equation giving its position ( upward) as a function of time . Assume the object started by being compressed 17 from the equilibrium position (where = 0), and released.

y(t)=(0.17m)?cos(2?t0.65s)

y(t)=(0.17m)?sin(2?t0.65s)

y(t)=(0.17m)?cos(0.65s?t)

y(t)=(0.17m)?cos(t0.65s)

Part B

How long will it take to get to the equilibrium position for the first time?

Express your answer to two significant figures and include the appropriate units.

Part C

What will be its maximum speed?

Express your answer to two significant figures and include the appropriate units.

Part D

What will be the object's maximum acceleration?

Express your answer to two significant figures and include the appropriate units.

Part E

Where will the object's maximum acceleration first be attained?

	release point
	equilibrium point

Solutions

Expert Solution

genius_generous answered 2 years ago

Next > < Previous

Related Solutions

A 10 10 kilogram object suspended from the end of a vertically hanging spring stretches the...

A 10 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 9.8 centimeters. At time ?=0 t = 0 , the resulting mass-spring system is disturbed from its rest state by the force ?(?)=70cos(8?) F ( t ) = 70 cos ( 8 t ) . The force ?(?) F ( t ) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. a) Determine the...

A 11.9-kg object oscillates at the end of a vertical spring that has a spring constant...

A 11.9-kg object oscillates at the end of a vertical spring that has a spring constant of 1.80 ✕ 104 N/m. The effect of air resistance is represented by the damping coefficient b = 3.00 N · s/m. (a) Calculate the frequency of the damped oscillation. Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? % (c) Find the time interval that elapses while the energy of the system drops to 3.00% of its...

You have a spring hanging vertically. You add a mass to the end and let it...

You have a spring hanging vertically. You add a mass to the end and let it stretch to find its new equilibrium position which is 3.17 cm below the unstretched position. You now raise the mass (compress the mass-spring system) to its original unstretched position. Now you release the mass. How far from this starting position does it travel downward until it stops and changes direction?

A 0.59-kg object connected to a light spring with a force constant of 22.2 N/m oscillates...

A 0.59-kg object connected to a light spring with a force constant of 22.2 N/m oscillates on a frictionless horizontal surface. The spring is compressed 4.0 cm and released from rest. (a) Determine the maximum speed of the object. m/s (b) Determine the speed of the object when the spring is compressed 1.5 cm. m/s (c) Determine the speed of the object as it passes the point 1.5 cm from the equilibrium position. m/s (d) For what value of x...

A mass hanging from a spring oscillates with a period of 0.35 s. Suppose the mass...

A mass hanging from a spring oscillates with a period of 0.35 s. Suppose the mass and spring are swung in a horizontal circle, with the free end of the spring at the pivot. What rotation frequency, in rpm, will cause the spring’s length to stretch by 15%?

Damping is negligible for a 0.155-kg object hanging from a light, 6.30-N/m spring. A sinusoidal force...

Damping is negligible for a 0.155-kg object hanging from a light, 6.30-N/m spring. A sinusoidal force with an amplitude of 1.70 N drives the system. At what frequency will the force make the object vibrate with an amplitude of 0.460 m? Lower frequency--? (in Hz) Higher frequency-- ? (in Hz)

A mass of 0.30 kg on the end of a spring oscillates with a period of...

A mass of 0.30 kg on the end of a spring oscillates with a period of 0.45 s and an amplitude of 0.15 m . A) Find the velocity when it passes the equilibrium point. B) Find the total energy of the system. C) Find the spring constant. D) Find the maximum acceleration of the mass.

When a body of mass 1.0 kg is suspended from a certain light spring hanging vertically, its length increases by 5 cm

When a body of mass 1.0 kg is suspended from a certain light spring hanging vertically, its length increases by 5 cm. By suspending 2.0 kg block to the spring and if the block is pulled through 10 cm and released, the maximum velocity of it in m/s is approximately

A 6.0 kg object attached to a horizontal spring oscillates with an amplitude A = 10...

A 6.0 kg object attached to a horizontal spring oscillates with an amplitude A = 10 cm and a frequency f = 2.2 Hz. (a) What is the force constant of the spring? _____N/m (b) What is the period of the motion? _____s (c) What is the maximum speed of the object? _____m/s (d) What is the maximum acceleration of the object? _____m/s2

A 8.50 kg mass is attached to the end of a hanging spring and stretches it...

A 8.50 kg mass is attached to the end of a hanging spring and stretches it 28.0 cm. It is then pulled down an additional 12.0 cm and then let go. What is the maximum acceleration of the mass? At what position does this occur? What is the position and velocity of the mass 0.63 s after release?

Subjects