Simple harmonic motion - vibration frequency


by Bugsy23
Tags: frequency, harmonic, motion, simple, vibration
Bugsy23
Bugsy23 is offline
#1
Oct18-10, 10:57 AM
P: 25
I need to calculate the frequency of sinusoidal vibrations in simple harmonic motion. The only known values that I have are the acceleration amplitude and the vibration amplitude. Is there a way of calculating the frequency of vibration without knowing the period of the oscillations?
Phys.Org News Partner Physics news on Phys.org
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Mapping the road to quantum gravity
Chameleon crystals could enable active camouflage (w/ video)
Andrew Mason
Andrew Mason is offline
#2
Oct18-10, 12:12 PM
Sci Advisor
HW Helper
P: 6,591
Quote Quote by Bugsy23 View Post
I need to calculate the frequency of sinusoidal vibrations in simple harmonic motion. The only known values that I have are the acceleration amplitude and the vibration amplitude. Is there a way of calculating the frequency of vibration without knowing the period of the oscillations?
The equation of motion is:

[tex]F = ma = m\ddot{x} = -kx[/tex]

The general solution is:

[tex]x = A_0\sin(\omega t + \phi)[/tex] where [itex]\omega^2 = k/m[/tex]

[itex]A_0[/itex] is the maximum amplitude of vibration (maximum x). The maximum acceleration occurs when x = ? What is the acceleration at that point? (hint: use the equation of motion to find maximum value for a).

From that you should be able to determine [itex]\omega[/itex]

AM


Register to reply

Related Discussions
Difficult problem about Simple Harmonic Motion using only mass to frequency ratios Introductory Physics Homework 2
Simple harmonic motion and frequency; answer disagrees from answer key Introductory Physics Homework 1
Deriving angular frequency for simple harmonic motion Introductory Physics Homework 2
axial, torsional and pendulum modes of vibration(harmonic motion) Introductory Physics Homework 0
simple harmonic frequency clarification Introductory Physics Homework 3