A spring oscillates vertically between positions A and B. Answer the following q

Question

A spring oscillates vertically between positions A and B. Answer the following questions regarding velocity, acceleration, kinetic energy, potential energy and total energy for the different positions. Match the correct answers to the questions. Answers may be re-used.

If spring is released from A.

Kinetic energy at 'A' =

Potential energy at x0 =

Total energy at 'B' =

Velocity at 'A'=

Acceleration at x0 =

Equation of motion =

A. Asin(2italic pi ft)

B. Acos(2italic pi ft)

C. (k/m)A

D. (1/2)kA2

E. 0

F. (1/2)kv2

Explanation / Answer

According to the given problem,

1.)Kinetic energy at 'A' -- Ans: 0 [E]

As its released from rest and no velocity

2.)Potential energy at x0 -- Ans: 0 [E]

As the spring is in its natural unstreched form

3.)Total energy at 'B' --- Ans: (1/2)kA2 [D]

As there is only elastic potensial energy due to spring contraction

4.)Velocity at 'A' --- Ans : 0 [E]

As there is only eastic potensial energy and no kinetic energy.

5.)Acceleration at x0 --- Ans : (k/m)A [C]

As its a simple hormonic motion,

6.) Equation of motion --- Ans : Acos(2italic pi ft) [B]

As its a simple hormonic motion,

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