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**

Join Physics Forums Today!

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

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

# Homework Help: SHM problem solving

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