Given equation X= 0.35 sin(5.50 t), mass m = 0.50
kg
comparing the equation with X= A Sin (wt), A is
amplitude, w is angular frequency = 2*pi*f, f is
frequency
A) Amplitude A = 0.35 m
B) frequency f = w/2pi = 5.50 / (2*3.14) = 0.8758
Hz
C) total energy E = 1/2 m w^2A^2 = 0.5 *0.5*5.5^2*0.35^2
= 0.9264 J
D) potential energy P.E = 1/2
kx^2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
w = sqrt(k/m) ==> k= w^2m = 5.5^2*0.5 = 15.125
                                Â
=
0.5*15.125*0.3^2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
                               Â
= 0.6806 J
total energy = kinetic energy + potential
energy
kinetic energy = total energy - potential
energy
                   Â
= 0.9264 -0.6806
             Â
K.E = 0.2458 J
