Blake Andrews
New member
- Joined
- Feb 12, 2020
- Messages
- 11
(a) Show that a particle is moving according to SHM if its displacement is given by x = 5cos 3t + 2sin 3t, where x is in metres and t is in seconds.
(b) Find the maximum speed.
(a) x = 5cos 3t + 2sin 3t
v = -15sin 3t + 6cos 3t
a = -45cos 3t - 18sin 3t
= -9(5cos 3t + 2sin 3t)
= -9x
Acceleration is proportional to displacement so the particle is moving according to SHM.
(b) I'm having trouble with this part. I was thinking of finding the equation for v in terms of x and then use v is max when x = 0:
1/2v2 = ∫-9x dx
= -9x2/2 + C
However i don't think i have enough information to find C.
Maybe i could find t when x = 0 and then find v but i'm not sure how to solve for t when 5cos 3t + 2sin 3t = 0
(b) Find the maximum speed.
(a) x = 5cos 3t + 2sin 3t
v = -15sin 3t + 6cos 3t
a = -45cos 3t - 18sin 3t
= -9(5cos 3t + 2sin 3t)
= -9x
Acceleration is proportional to displacement so the particle is moving according to SHM.
(b) I'm having trouble with this part. I was thinking of finding the equation for v in terms of x and then use v is max when x = 0:
1/2v2 = ∫-9x dx
= -9x2/2 + C
However i don't think i have enough information to find C.
Maybe i could find t when x = 0 and then find v but i'm not sure how to solve for t when 5cos 3t + 2sin 3t = 0