Simple Harmonic Motion [Part-III]

Only on the mass (m) and the spring constant (k), not on amplitude.

On what two factors does the angular frequency of SHM depend?

Fnet = ma = -kx

What does Newton’s 2nd law for a block on a spring state?

Weight (downward), normal force (upward), and spring force (horizontal).

What are the forces acting on the mass in a horizontal spring system?

They are equal and opposite, canceling each other out.

Why do weight and normal force not affect horizontal SHM?

m*((d^2)(x))/dt^2 = -kx

What is the equation of motion for the block on a spring?

((d^2)(x))/dt^2 = -(k/m)x

Rearranged, what does the acceleration equation become?

−Aω^2cos(ωt+ϕ)=−(k/m)Acos(ωt+ϕ).

By substituting motion equations, what relationship emerges?

ω = (k/m)^1/2

expression for angular frequency

T = 2π((m/k)^1/2)

What is the formula for the period of SHM?

Greater mass gives longer period (slower oscillation).

How does mass affect the period?

Stiffer spring (larger k) gives shorter period (faster oscillation).

How does spring stiffness affect the period?

f = 1/T = (1/2π)((k/m)^1/2)

Formula for frequency in SHM?

ω = 2π/T

How is angular frequency related to period?

The block oscillates in SHM.

What happens when a block is attached to a vertical spring and set in motion?

Because the block hangs freely; the spring itself balances the weight.

Why is there no normal force in the vertical spring case?

Gravity shifts the equilibrium position, but the period and frequency formulas remain the same as the horizontal case.

What is the effect of gravity in vertical spring SHM?