Question

0.33 Deduce an expression for the time period of the vertical oscillations of a massless
loaded spring. Does it depend on the acceleration due to gravity ?​

Answer 1

Answer:

Time period of the spring block system is given as

$T = 2\pi\sqrt{\frac{m}{k}}$

It is independent of the acceleration due to gravity

Explanation:

For vertical oscillation on spring block system we will have

at equilibrium position of the system

$mg = kx_o$

now when the mass is displaced by small distance "x"

we will have

$F = mg - k(x_o + x)$

now we have

$F = - kx$

so we have

$a = -\frac{k}{m} x$

so we have

$\omega = \sqrt{\frac{k}{m}}$

so we will have

$T = 2\pi\sqrt{\frac{m}{k}}$

It is independent of the acceleration due to gravity

#Learn

Topic: Spring block system

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