simple harmonics motion.... really appreciate your help.?

Question

Simple harmonic motion problem. "Simple harmonic" motion is oscillatory motion of the form x=x(o)*cos(2*pi*t / T), where x(o) is the maximum amplitude of oscillation and T is the period of oscillation.
EXAMPLE:
Find expressions for the velocity and acceleration of a car undergoing simple harmonic motion by differentiating x.
[Answer: a=–(2T)^2*x(o)cos(2*pi*t / T).]
(Find the expression for velocity on your own and make sure you understand how to derive the expression for acceleration.)
QUESTION:
If x(o) = 0.1 m and T = 5 s, what are the maximum values of velocity and acceleration?

Answer 1

For ease of typing, let xo = b
x = b.cos (2 π t / T)
Velocity
v = dx/dt = (- 2 π b /T).sin (2π t / T)
v = dx/dt = (- 2 π x 0.1 / 5) = - 0.126 (max. velocity)
Acceleration
a = d²x/dt² = (- 2 π b / T).(2π / T).cos (2π t / T)
a = ( - 4b / T²) (for max.)
a = - 0.4 / 25
a = - 0.016 m/sec² (maximum accn.)