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Question

A block of mass 2 kg attached to 3 springs as shown in figure.


What is the angular frequency of oscillation if mass m is slightly displaced from its equilibrium position ?
(Take, k=100 N/m)

A
12 rad/s
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B
8 rad/s
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C
5.5 rad/s
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D
10 rad/s
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Solution

The correct option is D 10 rad/s
Spring 1 and 2 are in series connection so that,

1k=1k1+1k2=12k+12k=1k

k=k

Now, spring k and spring 3 are in parallel connection with block m.

keq=k+k3=k+k=2k

The angular frequency of spring block system is given by

ω=keqm=2km

ω=2002=10 rad/s

Hence, option (D) is correct.

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