A very simple harmonic motion question (1 Viewer)

[kooltrainer]

1)A particle moving in SHM starts at the origin with velocity V. Prove that the particle first comes to rest after travelling a distance of V/n.

( i think n is used to find the period = 2pi/n)

 

[vds700]

1)A particle moving in SHM starts at the origin with velocity V. Prove that the particle first comes to rest after travelling a distance of V/n.

( i think n is used to find the period = 2pi/n)

x = asin(nt + A)
when t = 0, x = 0, therefore A = 0
x = asin nt
v = nacos nt
when t = 0, v = V
V =na
a = V/n

Therefore v = Vcos nt
it comes to rest when v = 0,
Vcos nt = 0
cos nt = 0
nt = pi/2
t = pi/(2n)....sub into x

x = (V/n)sin(n . pi/2n)
=(V/n)sin(pi/2)
=V/n

 

[3unitz]

x = A sin (nt)

v = An cos (nt)

when t = 0, v = V

.'. V = An

A = V/n

since the particle momentarily comes to rest at the amplitude of the motion, the particle first comes to rest after traveling the distance of the amplitude i.e. V/n

 

[lyounamu]

x = A sin (nt)

v = An cos (nt)

when t = 0, v = V

.'. V = An

A = V/n

since the particle momentarily comes to rest at the amplitude of the motion, the particle first comes to rest after traveling the distance of the amplitude i.e. V/n

Damn. I did that question and my working out was like Andrew's. Your working out makes it look so much simpler and easier to do...