Question

A spring and mass system are oscillating with an amplitude of 8.4 cm. The spring constant is 204 N/m and the mass is 540 g. Find the mechanical energy of the system to 2 sf.

Answer 1

x = .084 sin wt
max x = .084 when sin w t = 1
then
Pe = (1/2) k x^2 = (1/2) 204)(.084)^2

now what is Ke when sin wt = 1?

v = .084 w cos wt

if sin wt = 1, then cos wt = 0 because
sin^2 + cos^2 = 1 always
so
v = 0 when sin wt = 1
so
TOTAL energy = PE at sin wt = 1
= (1/2) (204)(.084)^2 Joules still