A 32pound weight stretches a spring 2 feet The weight is rel

A 32-pound weight stretches a spring 2 feet. The weight is released from rest at the equilibrium position. Find the equation of motion if an impressed force f(t)=20t acts on the system for 0t<5 and is then removed. Ignore any damping forces. Graph x(t) on the interval [0,10].

Use h(ta) for the Heaviside function shifted aa units horizontally.

Answer:
x(t)= _ _ _ _ _ _ _

Solution

In engineering applications, we frequently encounter functions whose values change abruptly at specified values of time t. One common example is when a voltage is switched on or off in an electrical circuit at a specified value of time t.

The value of t = 0 is usually taken as a convenient time to switch on or off the given voltage.

The switching process can be described mathematically by the function called the Unit Step Function (otherwise known as the Heaviside function after Oliver Heaviside).

SO x(t)= zero