DFD

1. Learning Objectives: Understandingthebasicconcepts of Simple Harmonic Motion, andtobecome
familiar with the terms commonly usedto define a simpleharmonic motionandits equation.
The displacement of a particle at t = 0.25 sis given by the expression
x = (4.0 m) cos(3.0 π t + π), where x is in meters and t is in seconds. Determine
(a) The frequency and periodof the motion,
(b) The amplitudeof the motion,
(c) The phaseconstant, and
(d) The displacementof the particle at t = 0.25 s
Solutions:
(a) Frequencyandperiodare quantitiesthatrelate to “angularfrequency”.The relationship
betweenangularfrequencyandperiodisthatangularfrequency(ω=2π/T), where T isperiod.
We thenget(2π/3π) = 2/3 = 0.66 seconds.Remember,the SIunitfor periodisinseconds.
Frequencycanbe relatedtoperiodbythe equationf = 1/T, we thengetf = 1 / (2/3) = 1.5 Hz.
Again,the SIunit forfrequencyisin“Hz”.
(b) Amplitude isthe terminfrontof the cosine expression.Inthiscase,itisgivenas4.0 meters.It
cannot be negative anddescribesthe maximumdisplacementof the oscillatorfromits
equilibriumposition. Itcontinuouslyvariesbetweenthe values –A and+A as the object
oscillates.
(c) The phase constant inthiscase isgivenasπ. The phase constantisan angle,measuredin
radians,itdeterminesthe startingangle of anoscillation.
(d) Thisquestionisaskingthatafter0.25s of oscillation,whatthe displacementis. The expression
nowbecomesx(t) =(4.0m) cos (3.0π * 0.25 + π),x(t) = 2.828m.