Question

5. A body oscillates with SHM along with X-axis. Its displacement varies with time
according to the equation : x = (4.00 m) cos(pie t + Pie/4)
Calculate at t = 1.00 S: (a) displacement (b) velocity (c) acceleration (d) Also
calculate the maximum speed and maximum acceleration and (e) phase at t =
2.00 s.​

Answer 1

Explanation:

Given,

x=5cos(2πt+π)

t=1.5sec

Displacement, x=5cos(2π×1.5+π)=5cos(4π)

x=5m. . . . . .(1)

Velocity, v=

dt

dx

v=−10πsin(2πt+π)

v=−10πsin(2π×1.5+π)

v=−10πsin(4π)

v=0m/s. . . . .(2)

Acceleration, a=

dt

dv

a=−20π

2

cos(2πt+π)

a=−20π

2

cos(2π×1.5+π)

a=−20π

2

cos(4π)

a=−20π

2