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Question

# A block attached to a spring with unknown spring constant oscillates with a period of 2.00 s. What is the period if a. The mass is doubled? b. The mass is halved? c. The amplitude is doubled? d. The spring constant is doubled? Parts a to d are independent questions, each referring to the initial situation.

Solution

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The equation for the period of an object attached to a spring is expressed as:

$T=2\pi \sqrt{\dfrac{m}{k}}=T_0=2.00\:s$

where $m$ is the mass and $k$ is the spring constant.

For part a) For mass= $2m$

$T=2\pi \sqrt{\dfrac{2m}{k}}=(\sqrt{2})T_0=2.83\:s$

For part b) For mass=$\dfrac{1}{2}m$

$T=2\pi \sqrt{\dfrac{\dfrac{1}{2}m}{k}}=T_0/\sqrt{2}=1.41\:s$

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