A spring oscillates vertically between positions A and B Ans

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

Solution

if the spring is released from A then

KE at A = 0

Ans(E)

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Potential energy at x0 = 0

Ans(E)

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total energy = k A^2 /2

Ans(D)

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velocity at A = 0   (extreme position)

Ans(E)
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at x0. spring is in natural length.

hence spring force = 0

and a = F/m = 0

Ans(E)

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motion starts from extreme position.

so at t = 0 , x = A

y = A cos(2 pi f t )

Ans(B)