SHM -6

Classical Mechanics Level 3

A mass spring system as shown in the picture is set up. The mass is displaced towards the right (i.e. the spring with spring constant k 1 k_1 is compressed). If the time period of the mass-spring system can be expressed as n π n \pi , find n n

Details and Assumption

k 1 = 2 N / m k_1 = 2 N/m

k 2 = 4 N / m k_2 = 4 N/m

m = 24 k g m = 24 kg

My apologies for the diagram.


The answer is 4.

Mehul Arora by Mehul Arora , 20, India

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1 solution

Yash Dev Lamba
Mar 3, 2016

k ( e q ) = k 1 + k 2 k_(eq) =k_1+k_2 = 2 + 4 = 6 N / m =2+4=6 N/m

Time period of spring mass system = 2 π m k ( e q ) 2\pi\sqrt{\frac{m}{k_(eq)}}

= 2 π 24 6 2\pi\sqrt{\frac{24}{6}} = 4 =4 π \pi seconds

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