PLEASE HELP ME ANSWER

Question

1. (a) Find the amplitude, frequency, and period of motion for an object vibrating at the end of a horizontal spring if the equation for its position as a function of time is x=(.52m)cos((𝜫/4) t) 

(b) Find the maximum magnitude of the velocity and acceleration. 

C) What are the position, velocity, and acceleration of the object after 2.00 s has elapsed?

Answer 1

The question does not mention the units of time t.

But since in part c) seconds are mentioned, I assume that t is measured in seconds.

(a)

Amplitude A is the maximum displacement, which is the constant multiplying cos,

i.e., A = 0.52 m.

Period T is the value of t that makes the argument of the cos equal 2π.

That is, (π/4)T = 2π

T = 8 s

Frequency f is the inverse of period

f = 1/8 s^-1

(b)

Velocity v is the derivative of displacement x, and

acceleration a is the derivative of velocity.

x(t) = 0.52cos((π/4)t)

v(t) = -0.52(π/4)sin((π/4)t)

a(t) = -0.52(π/4)²cos((π/4)t)

v_max = 0.52(π/4) = 0.4 m/s

a_max = 0.52(π/4)² = 0.32 m/s²

(c)

x(2) = 0.52cos((π/4)2) = 0

v(2) = -0.52(π/4)sin((π/4)2) = -0.52(π/4) = -0.4 m/s

a(2) = -0.52(π/4)²cos((π/4)2) = 0