Question

The equation of motion for a particular mass at the end of a spring is
x=0:40cos(0:70t−30)
m. For this oscillation, find the amplitude and the period.

a. 40 cm; 8.97 s
b. 20 cm ; 4.75s
c. 40 m; 9.87 s
d. 20 m; 4.75 s

Answer 1

Answer on Question#41351, Physics, Other

Question:

The equation of motion for a particular mass at the end of a spring is

$x = 0.40 \cos(0.70t - 30) \, \text{m}$ . For this oscillation, find the amplitude and the period.

a. $40 \, \text{cm}$ ; 8.97 s

b. $20 \, \text{cm}$ ; 4.75 s

c. $40 \, \text{m}$ ; 9.87 s

d. $20 \, \text{m}$ ; 4.75 s

Answer:

The general form of the sine function is:

$$y = A \sin (B x + C) + D$$

where:

$A$ is the amplitude of the function

The period of the function is: $T = \frac{2\pi}{B}$

Therefore, amplitude equals:

$$A = 0.4 \, \text{m} = 40 \, \text{cm}$$

And period equals:

$$T = \frac{2\pi}{0.7} = 8.97 \, \text{s}$$

Answer: a. $40 \, \text{cm}$ ; 8.97 s

http://www.AssignmentExpert.com/