Wednesday, 26 March 2025

Simple Harmonic Motion for A Level Physics: vertical motion of a spring

 

Simple Harmonic Motion - vertical motion of a spring

Upward force, T', when the stretched spring is released = k(e+x)
If the resultant force is F,
F = K(e+x) -mg
F = ma - Newton's Second Law
k(e+x) - mg = ma, where a is the acceleration
(ke + kx) - mg = ma
Since T = ke
mg - mg + kx = ma
ma = kx
a = k/m x
a ∝ x

ω2 = k/m

T =2π √(m/k)

T =2π √(m/k)

Since the acceleration is directly proportional to the displacement , the motion is SHM.

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