Question

A body of mass m hung at one end of the spring executes SHM. where K is the force
constant of the spring. prove that the relation given below is incorrect, also
derive correct relation.
T= 2πm/K​

Answer 1

Given:

A body of mass m hung at one end of spring which executes SHM.

K is the  spring constant .

To Find :

Time period of the S.H.M .

Solution:

Since the mass is in SHM

Let x = A Sin(wt +Ф)

Free body diagram of mass m

mg = downwards

Kx = spring force

where x is the displacement of mass m under action of  weight.

Inertial force on mass m = ma

ma + kx = 0

$a + \frac{kx}{m} = 0 \\x = Asin(\sqrt{\frac{k}{m} }t + \alpha )$

Compare with the displacement of mass in SHM .

$w = \sqrt{\frac{k}{m} } \\w = \frac{2\pi }{T} \\\\\sqrt{\frac{k}{m} } = \frac{2\pi }{T}\\ T = \frac{1\sqrt{\frac{k}{m} } }{2\pi }$

Time period of S.H.M= T =$\frac{1}{2\pi } (\sqrt{\frac{k}{m} } )$

Answer 2

Explanation:

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