Question

Prove for S. H. M. a=-w²x​

Answer 1

Answer:

If the total force F on a mass m follows Hooke's law,

F = −kx,

then one can use Newton's 2nd law

F=ma,

to infer that the motion is a simple harmonic motion

a=−ω2(square)x,

2π/T = ω =(square root)-/k/m ,

cf. OP's correct belief. Now it only remains to solve the ODE

d2(square)x(t)/dt2(square) = −ω2(square)x(t),

Explanation: