how to calculate time period of spring block systems

The Hooke’s law governing an ideal spring relates spring force with displacement as :
F=-kx --------------------------------------(i)
By Newton’s second law, F =ma --------------------------------(ii)
Combining with Newton’s second law,
?F=ma=-kx
so a = -kx/m -----------------------------(iii)
Now, comparing with SHM relation “ a = -?²x ”, we have : \
? - w² x = - kx/m
w² = k/m^\
w = squreroot (k/m)
since w =2pie/ T
theregore 2pie/T = squreroot (k/m)
T = 2pie squreroot (m/k)

The first step is to drive an equation between force and displacement or between acceleration and displacement. We, then, use standard expression to determine time period and frequency
for example

Combining with Newton’s second law,
f=ma=- kx
a=-k/m * x
Now, comparing with SHM relation
a=w² x

^{Thanks & Regards
Mukesh Sharma
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