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 3.2s . Parts A to D are independent questions, each referring to the initial situation.

A) What is the period if the mass is doubled?

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

B) What is the period if the mass is halved?

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

C) What is the period if the amplitude is doubled?

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

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

1.

T = 2pi sqrt(m/k)

T2 = 2pi sqrt(2m/k) = sqrt(2) * T

So, T2 = 1.414*3.2 = 4.5 sec

2.

If mass is halved

T2 = 2pisqrt(m/2k) = 1/sqrt(2) * T = 2.3 sec

3.

period is independent of amplitude

So, T will remain same = 3.2 sec

4.

If k is doubled

T2 = 2pisqrt(m/2k) = 1/sqrt(2) * T = 2.3 sec

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