SHM Qs (1 Viewer)

[doiyoubi]

A particle, moving with SHM has a velocity of 1.8m/s when passing theough its mean position, and the acceleration at 0.6m from the mean position is 2.4m/s². Find the amplitude and the period of the oscillation.

The acceleration of a particle moving in a straight line is given by d²x/dt²=2x-3, were x is the displacement, in metres, from the origin O and t is the time in seconds. Initally the particle is at rest at x=4.
(a) If the velocity of the particle is vm/s, show that v²=2(x^2-3x-4)
(b) Show that the particle does not pass through the origin.
(c) Determine the position of the particle when v=10

A particle is moving along the x axis and its velocity vm/s at the position x metres is given by v²=16+4x-2x²
(a) Show that the accleration at any time t is given by d²x/dt²=-2(x-1)
(b) Show that the motion is SHM
(c) Find the cntre and the period of the motion
(d) Find the amplitude of the motion
(e) Find the interval on the x axis for which the speed is >2rt2

Can someone help me on these thanks

 

[pLuvia]

2.
(a) d²x/dt²=(1/2v²)=2x-3
1/2v²=x²-3x+C
When v=0 x=4
C=-4
1/2v²=x²-3x-4
v²=2(x²-3x-4)

(c)When v=10
100=2x²6x-8
x²-3x-54=0
(x-9)(x+6)
x=9,-6 [x>]
.:x=9

3.
(a)
d²x/dt²
=dx/dt(1/2[16+4x-2x²]
=2-2x²
=-2(x-1)

(b)
a=-2(x-1)
SHM about x=1

(c)
Centre of motion when a=0
0=-2(x-1)
x=1
Period = 2pi/sqrt2

Hope that helped