What is the best way to go about solving a SHM problem that asks for amplitude and phase constant when only one initial condition (x(0)) is given? I'm a little confused because I read that to find A and the phase constant you must use the initial conditions - but I've encounter a few problems which only give one initial condition. I'm obviously missing some understanding... here's an example:(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

You observe a vibration that has a frequency of 45 Hz. At t = 0 the displacement is 20 mm and at t = 7 ms the displacement is -12 mm. What is the amplitude (A) and phase constant (⌀) for the equation x(t) = Acos(ωt + ⌀)

2. Relevant equations

x(t) = Acos(ωt + ⌀)

T = 1/f

ω = 2πf = 2π/T

3. The attempt at a solution

ω = 2πf

ω = 2π(45)

ω = 282.7 rads/s

x(t) = Acos(ωt + ⌀)

x(0) = 0.02 = Acos((282.7)(0) + ⌀)

0.02 = Acos(⌀)

A = 0.02/cos(⌀)

Now what? Do I do the same with x(0.007) even though A and ⌀ are supposed to be found using initial conditions?

Any help is appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# SHM problem solving

**Physics Forums | Science Articles, Homework Help, Discussion**