Question

A 0.502 kg air cart is attached to a spring and allowed to oscillate. The displacement of the air cart from equilibrium is given by x = 11.2 cm·cos(1.88t + π), where t is in seconds. Calculate the maximum kinetic energy of the cart.

Answer 1

Compare the given equation with standard equation

x = A*cos(w*t)

so,

Amplitude, A = 11.2 cm = 0.112 m

angular frequency, w = 1.88 rad/s

we know, Vmax = A*w

= 0.112*1.88

= 0.21056 m/s

so, KEmax = (1/2)*m*vmax^2

= (1/2)*0.502*0.21056^2

= 0.0111 J