Question

Derive the expression for time period of oscillation of a mass attached to a spring

Answer 1

Answer:

Period of a Mass on a Spring. The period of a mass m on a spring of spring constant k can be calculated as T=2π√mk T = 2 π m k .

Explanation:

Answer 2

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Consider a spring attached to one end of a block of mass m, and another end to the rigid support. Let 'm' be the mass.

$we \: know \: that \: \: f \: \alpha = x \\ f = - kx$

Where "K" is constant (spring constant)

From Newton's law.

$m.a = - kx \\ a = - ( \frac{k}{m} )x$

But Acceleration of particle executing SHM is

$a = - {w}^{2} x \\ {w}^{2} = ( \frac{k}{m} ) \\ ➻ \: \: \: w = \sqrt{ \frac{k}{m} }$

$➻ \: \: \: \: \: w = \frac{2\pi}{t} \\ \: \: \: \: \: \: \: \: \: \: ➻ \: \: \: \: \: \: \: \: \: \frac{2\pi}{t} = \sqrt{ \frac{k}{m} } \\ \\ t = 2\pi \sqrt{ \frac{m}{k} }$

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