The position of a particle is given by theexpression x =(4.00 m) cos(5.00 t + ),

Question

The position of a particle is given by theexpression x =(4.00 m) cos(5.00t + ),where x is in metersand t is in seconds. (a) Determine the frequency and period of themotion.
___ Hz
___ s

(b) Determine the amplitude of themotion.
___ m

(c) Determine the phase constant.
___ rad

(d) Determine the position of the particleat t = 0.250 s.
___ m (a) Determine the frequency and period of themotion.
___ Hz
___ s

(b) Determine the amplitude of themotion.
___ m

(c) Determine the phase constant.
___ rad

(d) Determine the position of the particleat t = 0.250 s.
___ m

Explanation / Answer

f = /2 =(5/2) = 5/2 T = 1/f = 2/5 amplitude = A = 4.00m phase constant = pi radians 4.00cos(5*.250 + ) = 2.83 meters To solve these problems, you need to look at the equation for theposition function of SHM x = Acos(t+) where A = amplitude = angular frequency = phase constant the velocity function for SHM is simply the derivative of this andthe acceleration function is the derivative of the velocity.

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