Kinematics of simple harmonic motion Intro: Let’s look at how the initial condit

Question

Kinematics of simple harmonic motion

Intro:
Let’s look at how the initial conditions determine the amplitude and phase constant of SHM.
Given: period T or angular frequency w, initial position x(0) and initial velocity vx(0) at t=0
Find: amplitude A and phase constant 0
The displacement from equilibrium as a function of time x(t) is represented as
x(t)=A cos(wt+0) (1)
Then, the x-component of velocity vx(t)=dx/dt
vx(t)= -Aw*sin(wt+0) (2)
Suppose T=2.0s, then the cycle frequency f=1/T=0.5 Hz and angular frequency w=2pi/T=3.14 rad/s.

Homework problem 1 (10 points)
Study the examples above and use the same approach to determine A and 0 for the following initial
conditions:
x(0)=+1.0 m and vx(0)=+1.0 m/s.
1. Give expressions for x(t) and v(t), explicitly showing what And 0 are. Show your work.

I just want to get . If you guys solve this problem, plz show me the detail soultion.

Thanks!

Explanation / Answer

x(t)=A cos(wt+0)

v(t)= -Awsin(wt+pi/2)

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