A mass weighing 24 pounds stretches a spring 4 feet The subsequent motion takes place in medium that offers a damping force numerically equal to ( 0) times the instantaneous velocity If the mass is initially released from the equilibrium position with an upward velocity of 2 ft s, show that when 32...

The equation of motion for the massspring system is given by m x x kx 0 where m is the mass k is the spring constant is the damping coefficient x is t ...

A mass weighing 24 pounds stretches a spring 4 feet. The subsequent motion takes place in medium

Question:

A mass weighing 24 pounds stretches a spring 4 feet. The subsequent motion takes place in medium that offers a damping force numerically equal to β(β 0) times the instantaneous velocity. If the mass is initially released from the equilibrium position with an upward velocity of 2 ft/s, show that when β > 3√2 the equation of motion is

-3 x(t) VB2 - 18 2B1/3 sinh 2 VB² -18t. e