Question

The displacement h(t) in centimeters of a mass suspended by a spring is modeled by the function h(t) = 1/4sin(120(pi)t), where t is measured in seconds. Find the amplitude, period, and frequency of this displacement.

Please help!

Answer 1

• amplitude: 1/4 cm
• period: 1/60 second
• frequency: 60 Hz

Explanation:

The amplitude is the multiplier of the sine function: 1/4 cm.

The period is the value of t that makes the argument of the sine function be 2π:

(120π rad/s)t = 2π rad

t = (2π rad)/(120π rad/s) = 1/60 s

The frequency is the reciprocal of the period: 1/(1/60 s) = 60 Hz.

Answer 2

Amplitude is the first value given = 1/4

Frequency is found using: ω = 2(pi)f

ω is given in the equation as 120 pi

Solve for f:

120PI = 2PIf

f = 120pi / 2PI

f = 60

Frequency = 60

The period is the reciprocal of the frequency:

Period = 1/60