Fill in the blanks

Question

A particle does simple harmonic motion along

x-axis, amplitude is 0.12m, period is 2s, when t=0, 

the displacement relative to equilibrium position is 0.06m, the particle moves positively to x-axis at the moment. Then, the angular frequency is_______,

The frequency is ________, the equation of the SHM  is ___________, the maximum value of the velocity of SHM is _________, and the maximum value of the acceleration of SHM is_________.

 

 

Answer 1

For a simple harmonic oscillator:

• Angular frequency = 2pi/period
• Frequency = 1/period
• x(t) = (amplitude)·sin(angular frequency(t - initial displacement))  where t is time.  Assumes equilibrium position is at x = 0
• Velocity = dx(t)/dt = (amplitude)·(angular frequency)·cos(angular frequency(t - initial displacement)).  Max value occurs when the |cosine| = 1
• Acceleration = dVelocity/dt = -(amplitude)·(angular frequency)²·sin(angular frequency(t - initial displacement)).  Max value occurs when |sine| = 1