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Unformatted text preview: position function: v(t) = dx/dt = - x m ω sin( ω t + φ ) It takes the maximum value of x m ω . Therefore, the maximum velocity is given by v m = x m ω . According to the graph, the maximum velocity is 25 cm/s. The angular frequency is ω = v m /x m = 10 rad/s b) What is the phase constant (from 0 to 2 π rad) for the harmonic oscillator? The velocity and acceleration of the oscillator are v(t) = dx/dt = - v m sin( ω t + φ ) , a(t) = dv/dt = -a m cos( ω t + φ ) At time t = 0, the velocity takes the value v s = 40 cm/s. The velocity function yields v s = -v m sin( φ ) ⇒ φ = sin-1 (-v s /v m ) = 4.07 rad, 5.36rad At time t = 0, the acceleration (i.e. the slope of the graph) is positive. The acceleration function yields -a m cos( φ ) > 0 π /2< φ <3 π /2 Therefore, the phase constant is 4.07 rad....
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This note was uploaded on 12/10/2011 for the course PHY 2048 taught by Professor Field during the Spring '08 term at University of Florida.
- Spring '08