differential Equations A spring with an 8 kg mass is kept st

differential Equations

A spring with an 8 kg mass is kept stretched 0.4 meter beyond natural length by a torce of ition and is ven an initial elocitvof 1m/s. 32 N. The spring starts at its equilibrium posi Find the pat ion of the mass at any time t

Solution

Force constant, k of spring is given by k = 32/0.4 = 80 N/m
Time period, T of oscillation = 2*pi*sq rt (m/k) = 2*pi*sqrt(8/80)
Angular frequency,\"omega\" = 2*pi/T = sqrt(80/8) = 2.828 rad/s
maximum velocity = 1 m/s = (amplitude, A)*omega or
A = 1/omega = 0.3535 m
displacement \'x(t)\' at any time \'t\' is given by
x(t) = 0.3535*sin[2.828*t]