Question

Simple harmonic oscillation is a type of motion that obeys the equation dar dt where co is called the angular frequency of the oscillation. Assume that we have a spring-mass system with a spring constant k and mass m. Find the angular frequency of the oscillation of the mass about its equilibrium position.

Answer 1

dx²/dt² = - w² x

Since a = dx²/dt²

hence

a = -  w² x Eq-1

k = spring constant of the spring

m = mass attached to the spring

when the mass is at distance "x" from the equilibrium position , spring force on the mass attached is given as

F = - k x

acceleration of the mass attached is given as

a = F/m

a = - k x/m

a = - (k/m) x Eq-2

comparing Eq-1 and Eq-2

w² = k/m

w = sqrt(k/m)