Question

The period of oscillation of a spring-and-mass system is 0.610 s and the amplitude is 4.47 cm. What is the magnitude of the acceleration at the point of maximum extension of the spring? in m/s²

Answer 1

The displacement of mass from equilibrium position in a spring mass system is given by

= A sin(wt+0)

The velocity of the mass is the time derivative of the displacement

v= =wAcos(wt+)

The acceleration of the mass is the time derivative of the velocity

= -w2A sin(wt + o)

$a=-\omega^2 x$

The angular frequency is related to the time period of oscillation as

$\omega=\frac {2\pi}{T}$

W = - = 10.3 rad/s

The maximum extension or the amplitude of the oscillations is x=A=4.47cm=0.0447m. The acceleration at the point of maximum extension is

7 =D

a = (10.3 rad/s)2 x (0.0447 m)

a = 4.74 m/s2