# A 200 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x = 5.0 cm and has vx = -30 cm/s.   Write down an equation that describes the position...

A 200 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x = 5.0 cm and has vx = -30 cm/s.

Write down an equation that describes the position of the oscillating mass as a function of time ( ie. what is x(t)? ).

jerichorayel | Certified Educator

In dealing with Oscillatory Motion, we should take note of the following terms:

P = period
f = frequency
`omega` = angular frequency
v = speed
A = amplitude
E = energy
x = length
`phi` = phase constant
t = time

For example, a mass X kg has a periodic, sinusoidal motion on the x axis, and its motion takes from x = +A and x = −A. The general expression for x (t) would be:

`x(t) = A cos(omega*t + phi)`

Since `omega = sqrt(k/m) = 2*pi*f = (2*pi)/T` , we can substitute these expressions based on the given values in the problem.

For velocity, the expression would be:

`v(t) = dx/dt = -omega A sin(omega*t + phi)`