An Object moves in a simple harmonic motion described by the equation d = 1/3 si

Question

An Object moves in a simple harmonic motion described by the equation d = 1/3 sin 6t where t is measured in seconds and d in inches. Find maximum displacement, the frequency, and the time required for one cycle. Find the maximum displacement. in. (Type an integer or a fraction.) b. Find the frequency. Cycles per second (Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the expression.) c. Find the time required for one cycle, sec. (Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the expression.)

Explanation / Answer

simple harmonic equation = 1/3 sin 6t

an object that moves in a simple harmonic motion if its distance from origin is d at a time t is given by

d =a cos wt or d = a sin wt

where a is the maximum displacement of the object from rest position

in this case 1/3 sin 6t maximum displacement is 1/3

b) frequency is the multiplier of t

so here multiplier of t is 6

frequency = 6

c) time required to complete one cycle will be given by 2pi/ frequency

2pi/ 6 = pi/3

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