Asked by sarah
A 300g particle oscillating in SHM travels 11cm between the two extreme points in its motion with an average speed of 65 cm/s.
a) Find the angular frequency
b)The maximum force on the particle
c)The maximum speed
a) Find the angular frequency
b)The maximum force on the particle
c)The maximum speed
Answers
Answered by
bobpursley
a. period=11/65 seconds
angular freq=2PI/period=w
b. force=mass*acceleration
I assume you know a little calculus. Amplitude is 11/2
displacement=amplitude*sin(ang freq *time)
taking the derivative, w=angfreq
velocity= wA*cos(wt)
taking the second derivative
acceleration=-Aw^2sin(wt)
max acceleration=-A w^2
max force= mass*maxacceleration
max velocity (above) when cosine is 1, so vmax=wA
angular freq=2PI/period=w
b. force=mass*acceleration
I assume you know a little calculus. Amplitude is 11/2
displacement=amplitude*sin(ang freq *time)
taking the derivative, w=angfreq
velocity= wA*cos(wt)
taking the second derivative
acceleration=-Aw^2sin(wt)
max acceleration=-A w^2
max force= mass*maxacceleration
max velocity (above) when cosine is 1, so vmax=wA
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