Figure below shows a mass $m$ suspended with a massless inextensible string passing over a frictionless pulley. The spring constant is $k$ , what is the time period of oscillations of the mass?

2 π \sqrt{m / 2 k}

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2 π \sqrt{m / k}

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2 π \sqrt{2 m / k}

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Solution

The correct option is D $2 π \sqrt{m / k}$
Here, the pull on the spring will be
$F = T = m g = k y$ ,
where $y$ is the extension of the spring
Hence, time period $= 2 π \sqrt{\frac{y}{g}} = 2 π \sqrt{\frac{m}{k}}$ .

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Figure below shows a mass m suspended with a massless inextensible string passing over a frictionless pulley. The spring constant is k, what is the time period of oscillations of the mass?

The correct option is D 2π√m/kHere, the pull on the spring will beF=T=mg=ky,where y is the extension of the springHence, time period =2π√yg=2π√mk.

Figure below shows a mass $m$ suspended with a massless inextensible string passing over a frictionless pulley. The spring constant is $k$ , what is the time period of oscillations of the mass?

The correct option is D $2 π \sqrt{m / k}$
Here, the pull on the spring will be
$F = T = m g = k y$ ,
where $y$ is the extension of the spring
Hence, time period $= 2 π \sqrt{\frac{y}{g}} = 2 π \sqrt{\frac{m}{k}}$ .