The position of a particle is given by the expression x = 2.00 cos (6.00 pi t+pi

Question

The position of a particle is given by the expression x = 2.00 cos (6.00 pi t+pi/2), where x is in meters and t is in seconds. Determine the frequency. Hz Determine period of the motion. S Determine the amplitude of the motion. M Determine the phase constant. rad Determine the position of the particle at t = 0.330 s. m A simple harmonic oscillator takes 10.0 s to undergo four complete vibrations. Find the period of its motion. S Find the frequency in hertz. Hz Find the angular frequency in radians per second. Rad/s

Explanation / Answer

2a) compsring it with equation x(t) = A Sin (wt+phase)

wt= 6Pi

2xpixf=6xpi

f=3hz

b)period = 1/f = 0.333 sec

c) Amplitude = 2

d) phase constant = pi/2

position at 0.330 is

=2 sin( 0.330*6*pi+pi/3)

= 1.988

3) a) 10 second to Undergo 4 oscillation .
Period = 10/4 = 2.5s

b) Frequency = 1/ Period .
= 1/2.5= 0.4 Hz.

c) Angular frquency = (angle in radians)X(Frequency)
=(2(pi))X(0.4)
=2.512 radians per second.

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