Question

By s h m method fond expression of acceleration and velocity

Answer 1

Question:-

Derive an expression of acceleration and velocity by S.H.M. method.

Answer:-

Differential equation of Linear S.H.M. :

$\large\rm{ d^{2} x/dt + (k/m)x = 0}$

✨Units:

$\large\rm { d^{2} x/dt }$ → Acceleration

$\large\rm { x}$ → Displacement

$\large\rm { m}$ → mass of body

$\large\rm { k}$ → Force constant

Now, we know that, $\large\rm { k/m = \omega^{2}}$

✨Unit:

$\large\rm { \omega}$ → angular frequency

Now,

$\large\rm { \therefore d^{2} x/dt + \omega^{2}x = 0}$

$\large\rm { a \ of \ S.H.M. = d^{2} x/dt = - \omega^{2} x}$