Question

A 0.500-kg mass suspended from a spring oscillates with a period of 1.36 s. How much mass must be added to the object to change the period to 2.04 s?

Answer 1

The mass that must be added is 0.628 kg

Explanation:

The period of a mass-spring system is given by

$T=2\pi \sqrt{\frac{m}{k}}$

where

m is the mass

k is the spring constant

For the initial mass-spring system in the problem, we have

m = 0.500 kg

T = 1.36 s

Solving for k, we find the spring constant:

$k=(\frac{2\pi}{T})^2 m = (\frac{2\pi}{1.36})^2 (0.500)=10.7 N/m$

In the second part, we want the period of the same system to be

T = 2.04 s

Therefore, the mass on the spring in this case must be

$m=(\frac{T}{2\pi})^2 k =(\frac{2.04}{2\pi})^2 (10.7)=1.128 kg$

Therefore, the mass that must be added is

$\Delta m = 1.128 - 0.500 = 0.628 kg$

Learn more about period:

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