Splung.com Physics Forum Forum Index Splung.com Physics Forum
Discuss physics or ask questions. Part of the Splung.com physics web site.
 
   SearchSearch   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

Hamonic Motion

 
Post new topic   Reply to topic    Splung.com Physics Forum Forum Index -> Physics Help. Ask a Physics Expert
View previous topic :: View next topic  
Author Message
mjgillen08



Joined: 22 Feb 2010
Posts: 1
Location: Illinois

PostPosted: Mon Feb 22, 2010 11:27 pm    Post subject: Hamonic Motion Reply with quote

A 12kg body undergoes simple harmonic motion of amplitude 8.5cm and period .2 seconds.What is the magnitude of the maximum force acting on it?


Thanks for the help!
Back to top
View user's profile Send private message
hepcj
Site Admin


Joined: 23 Jun 2007
Posts: 125

PostPosted: Tue Feb 23, 2010 1:25 am    Post subject: Reply with quote

The maximum force occurs when there is the greatest acceleration.

The definition of SHM is that the displacement is in opposition to the acceleration. i.e. x = - k a

Maximum acceleration occurs when the body is at the fullest extent of travel and is just about to change direction.

From the mathematical description of SHM displacement, acceleration is the second derivative of the displacement:

displacement: x(t) = A sin(omega t)
velocity: x'(t) = A*omega cos (omega*t)
acceleration: x''(t) = - A*omega^2 sin(omega*t)

f =1/T = omega/(2pi)
therefore,

omega = 2pi/ T


at the end of the swing the sin(omega t) =1 so
accleration: x''(t) =-A*omega^2 or A*(2pi/T)^2


m=12kg
A=8.5cm = 0.085 m (got to convert to metre so the units work out.)
T=0.2 sec

Substituting the above values into equation for acceleration:
magnitude of a = 0.085 * (2*pi/0.2)^2 = 83.89 ms^-2

and from F= ma
F= 12* 83.89 = 1007 N
Back to top
View user's profile Send private message Send e-mail
Display posts from previous:   
Post new topic   Reply to topic    Splung.com Physics Forum Forum Index -> Physics Help. Ask a Physics Expert All times are GMT
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum


© Copyright 2010 Splung.com