An object is attached to a spring on a frictionless horizontal surface. The obje

Question

An object is attached to a spring on a frictionless horizontal surface. The object is pulled to the right and released from rest at t = 0 s. If the object reaches a maximum speed of 34.5 cm/s and oscillates with a period of 3.00 s, what is the object's position at t = 0.450 s?

An object attached to a vertical spring is displaced 10.4 cm from rest and then released. If the mass oscillates 32.0 times in 23.9 s and the spring constant in the spring is 25.5 N/m, what is the mass of the object?

A 1.32 kg ball is attached vertically to a spring with a spring constant of 16.9 N/m. The wooden block is pulled down from rest and then released. What is the initial amplitude of oscillation if the ball's amplitude of oscillation is decreased to 2.30 cm after 26.0 oscillations and the time constant is 43.2 s?

Explanation / Answer

The object will be SHM

We know that in SHM maximum speed is

A

So,

A=0.345 m/s

Also,

it is given that time peroid is 3 s

so

T=2/

=6.28/3

=2.93 rad/s

So,

A=0.345

A*2.93=0.345

A=0.118 m or 11.8 cm

Now equation of motion of SHM is

x=Acost

so at t=0.45 s

x=11.8 cos(2.93*0.45)

x=11.79 cm.

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