A block attached to a spring with unknown spring constant oscillates with a peri

Question

A block attached to a spring with unknown spring constant oscillates with a period of 1.8 s . Parts A to D are independent questions, each referring to the initial situation.

Part A

What is the period if the mass is doubled?

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

Part B

What is the period if the mass is halved?

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

Part C

What is the period if the amplitude is doubled?

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

Part D

What is the period if the spring constant is doubled?

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

Explanation / Answer

Time period of oscillation of a block attached to a spring = 1.8 s

The formula for time period of oscillation, T = 2* sqrt (m/k)

where, m is the mass of the block

  k is spring constant

PART-A

When mass 'm' is doubled, so m = 2m

then T' = 2* sqrt (2m/k)

= sqrt (2) * 2* sqrt (m/k)

= sqrt(2). T

= sqrt (2) * 1.8

So, T' = 2.54 s

PART-B

When mass 'm' is halved, so m = m/2

then T' = 2* sqrt (m/2k)

= sqrt (1/2) * 2* sqrt (m/k)

= sqrt(1/2). T

= sqrt (1/2) * 1.8

= 1.27 s

So, T' = 1.27 s

Part C

Since time period is independent of amplitude, the time period remains the same

T=1.8 s

Part D

When spring constant 'k' is doubled, k=2k

then T' = 2* sqrt (m/2k)

= sqrt (1/2) * 2* sqrt (m/k)

= sqrt(1/2). T

= sqrt (1/2) * 1.8

= 1.27 s

So, T' = 1.27 s

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