Question

The function x = (7.8 m) cos[(5πrad/s)t + π/3 rad] gives the simple harmonic motion of a body. At t = 4.4 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion?

Answer 1

Answer:

a.3.84m

b.-106.67m/s

c.947.3m/s^2

d.70.17 rad

e.2.5Hz

d.0.4secs

Explanation:

Given x=(7.8)cos[5πrad/s)t+π/3)]

a.Displacement at t=4.4

7.8cos(5π*4.4+π\3)=3.84m

b.velocity

V= dx/dr=-5π(7.8)sin(5πrad/s)t+π\3

at t=4.4

-5π(7.8)sin(5π*4.4+π\3)=-106.67m/s

c.acceleration

a=d^2x/dr^2

-(5π)^2(7.8) cos (5π*t+π\3)

at t=4.4

-(5π)^2(7.8)cos(5π*4.4+π\3)=-947.3m/s^2

d. Phase =(5πrad/s)t+π\3

At t=4.4

5π×4.4+π\3=70.17 rad

e.frequency

Given x= 7.8cos(5πt+π\3

Compare with x=Acos(2πft)

2πft=5πt

F=2.5Hz

f.T=1\f

T=1/2.5=0.4sec