Question

A spring-mass system is subjected to a step force of magnitude 2m, where m is the mass of the vibrating system. Determine the maximum acceleration response of the system.

Answer 1

2 m/s²

Step-by-step explanation:

Given;

Magnitude of the force, F = 2m

mass of the vibrating system = m

Now,

The step force is given as;

F = kA

where, k is the spring constant

A is the amplitude of the vibration

therefore,

A = (F / k)

or

A = (2m / k)

also,

Acceleration, a = Aω²

where,

ω is the angular velocity = √(k / m)

therefore,

a = A × √(k / m)²

or

`a=(2m)/(k)*(k)/(m)`

or

a = 2 m/s²