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?

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