- #1
Awer1
- 5
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If the phase angle for a block-spring system in SHM is φ and the block's position is given by x = xm cos(ωt+φ), what is the ratio of the kinetic energy to the potential energy at time t = 0? State your answers in terms of the given variables.
x =xm Cos(wt + phi)
v = -w(xm)sin(wt +phi)
K = (1/2 mv2)
P = (1/2 m w2 x2)
dividing K/P = [v/wx]2
substitute v and x we get: [(-w(xm)sin(wt +phi)/(w)(xm Cos(wt + phi))]2
simplifying we get: [-wtan(wt + phi)/w]2 = [tan(wt + phi)]2
at t = 0 we should get the following: [v/wx]2 = [tan(phi)]2
The answer is marked wrong, am I interpreting the question incorrectly? I know what ratio is.. and ratio for Kinetic energy and Potential should be K/P right?
x =xm Cos(wt + phi)
v = -w(xm)sin(wt +phi)
K = (1/2 mv2)
P = (1/2 m w2 x2)
dividing K/P = [v/wx]2
substitute v and x we get: [(-w(xm)sin(wt +phi)/(w)(xm Cos(wt + phi))]2
simplifying we get: [-wtan(wt + phi)/w]2 = [tan(wt + phi)]2
at t = 0 we should get the following: [v/wx]2 = [tan(phi)]2
The answer is marked wrong, am I interpreting the question incorrectly? I know what ratio is.. and ratio for Kinetic energy and Potential should be K/P right?