2 simple harmonic motion (1 Viewer)

[jemsta]

if u can help that would be greatly appreciated
1) a point moves with SHM, if when at distances of 3 and 4cm from the centre of its path, its velocities are 8cm and 6cm respectively, find its period and its acceleration when at its greatest distance from the centre

2) a particle moving with simple harmonic motion makes 10 complete oscillations per minute. its max speed is 5m/s. what is the time taken to move from full amplitude to half amplitude?

 

[FinalFantasy]

if u can help that would be greatly appreciated
1) a point moves with SHM, if when at distances of 3 and 4cm from the centre of its path, its velocities are 8cm and 6cm respectively, find its period and its acceleration when at its greatest distance from the centre

1. let x=asin nt
v=ancos nt

4\a=sin nt
6\an=cos nt
16\a²+36\a²n²=1
16+36\n²=a²

3\a=sin nt
8\an=cos nt
9\a²+81\a²n²=1
9+81\n²=a²

so 16+36\n²=9+81\n²
45\n²=7
n²=45\7
n=sqrt (45\7)
T=2pi\n

sub n back into one of dem to find a
den "acceleration when at its greatest distance from the centre"
is when x=a
just use x''=-n²x !!

 

[FinalFantasy]

2) a particle moving with simple harmonic motion makes 10 complete oscillations per minute. its max speed is 5m/s. what is the time taken to move from full amplitude to half amplitude?

"10 complete oscillations per minute"
so one 10 oscillations per 60 seconds
10\60 oscillations per second
so period, T=1\6=2pi\n
.: n=12pi

let x=asin 12pit
v=12pia cos 12pit
"its max speed is 5m/s."
.: 12pi a=5
a=5\12pi
.: half amplitude=5\24pi
at x=a, t=1\24
at x=5\24pi
5\24pi=5\12pi sin 12pi t
1\2=sin 12pit
12pi t=pi\6, 5pi\6
t=1\72, 5\72

so time taken from full amp to half amp is
5\72-1\24=1\36 seconds

alrite hopefully no mistake dis time

 

[mattchan]

Btw, isnt Period, time for one oscillation? So in the 2nd question, one oscillation occurs in 6 seconds?

 

[FinalFantasy]

^
ur rite!
omg i've been sooo stupid lately, sooo many silly things i do....