The Period and Sinusoidal Nature of SHM 01

What is the general equation for SHM?

x(t)=A cos(ωt+ϕ)

What does the term “sinusoidal nature” mean?

It means displacement, velocity, and acceleration vary smoothly with time following sine or cosine curves.

What is the period of SHM?

T=2π/ω​=2π sqrt(m/k)​​

What is the frequency of SHM?

f= 1/T​= ω​/2π

How is SHM related to circular motion?

SHM is the projection of uniform circular motion on one axis.

What is the velocity equation in SHM?

v(t)= −Aωsin(ωt+ϕ)

What is the acceleration equation in SHM?

a(t)=−Aω²cos(ωt+ϕ)=−ω²x

What is the phase relationship between x, v, and a?

• Velocity leads displacement by 90° (π/2).

• Acceleration is opposite in phase (180° out) with displacement.

What happens to acceleration and velocity at extreme points?

• At x = ±A: velocity = 0, acceleration = maximum.

• At x = 0: velocity = maximum, acceleration = 0.