Question

Derive the differential formula for SHM

Answer 1

1sr formula............

T = 2phi under root m/k
Here m is mass of objects in kg
Here k is spring constant of spring
Here that is time period of oscillation in seconds

2nd formula..............

X = a sin cot
X = displacement in meter
A = amplitude in meter
Sin = angular frequency in radias per seconds
Cot = time is second

Answer 2

By defn of SHM
F=kx........... (1)
Where k=force constant
By Newton second law of motion
F=ma........(2)
a=acceleration deu to gravity
From equation 1 and 2

Kx=ma

$a= {d}^{2} x \div d {v}^{2}$
d^2x/dt^2=(k/m)x
But k/m=w^2
dx^2/dt^2=w^2x