A block of mass is attached to a horizontal spring of force constant on a smooth table
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A block of mass 0.50kg is attached to a horizontal spring of force constant 80Nm−1 on a smooth table. A dashpot exerts a damping force proportional to the velocity with damping coefficient 4kgs−1. A horizontal force F(t)=5cos6tN acts along the line of the spring.
(i) Taking the displacement x(t) of the block to the right as positive, derive the differential equation of motion of the block.
(ii) Write the equation that would govern the motion if the dashpot were removed, and hence obtain the natural angular frequency of the system.
(iii) Prove, by performing dimensional checks, that every term in the equation obtained in part (i) has the dimensions of force.