Question

The force-constant of an ideal spring is 200 Nm^-1.
A body of mass (200/pie^2) kg is suspended from it
and is made to oscillate. Find the time period of the
oscillation.
​

Answer 1

Given:-

The force constant of an ideal spring is 200 Nm-¹. A body of mass is 200/π² kg is suspended from it and to oscillate.

To Find:-

What is the time period of the oscillation.

Formula Used:-

${\pink{\boxed{\large{\bold{T =\: 2{\pi}\sqrt{\dfrac{m}{k}}}}}}}$

where,

• T = Time Period

• m = Mass

• k = Spring Constant

Solution:-

Given :

$Mass = </p><p>\sf \dfrac{200}{{\pi}^{2}}$

Spring Constant = 200 Nm-¹

According to the question by using the formula we get,

$\sf T =\: 2{\pi}\sqrt\dfrac{\cancel{200}}{{\pi}^{2} \times \cancel{200}}$

$\sf T =\: 2{\pi}\sqrt\dfrac{1}{{\pi}^{2}}$

$\sf T =\: \dfrac{2\cancel{{\pi}}}{\cancel{{\pi}}}$

$\sf T =\: \dfrac{2}{1}$

T=2 seconds

The time period of the oscillation is 2 seconds .