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Question

A spring block system (mass m, spring constant k) is placed on a smooth inclined plane of inclination θ. The inclined plane is accelerated horizontally such that the block does not loose contact with the surface. The time period of small oscillation of the block is

A
2πmk
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B
2πm sin θk
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C
2πmgka
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D
2πmk sin θ
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Solution

The correct option is A 2πmk
Let x0 be the elongation of spring in equilibrium


ma cos θ+mg sin θ=kxo(1)

Let x be displacement of mass from equilbrium

Fnet=mgsinθ+ma cos θk(xo+x)=kx
anet=kxm
As aω2x
mass executes SHM
ω=km
T=2πmk

OR

mg and Pseudo - force (ma) do not contribute to the restoring force. Hence the time period of the block does not change and =2πmk

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