Question

lp

Answer 1

I got x(t)=Acos(bt) so far but what would I do next

Answer 2

Here is our differential equation:
$$\large
F = m a = m \frac{\mathrm{d}^2x}{\mathrm{d}t^2} = -k x.
$$
Substitute for x(t) (this is our guess):
$$\large
x(t) = A\cos\left( \omega t+\phi\right)
$$
Where
$$
\large{
\omega = \sqrt{\frac{k}{m}} = \frac{2\pi}{T}
}
$$
and \(\phi\) is the phase (which is determined by the initial position of the spring).

Hope this helps.

Answer 3

Note A is the maximum displacement, \(\omega\) is the angular frequency of oscillation in radians per second and T is the period of oscillation.

Answer 4

@butterflyprincess, can you differentiate x(t)?

Answer 5

still a bit confused

Answer 6

so I differentiate the equation given above ?

Answer 7

yeah, with respect to t

Answer 8

Oh so... this one ? x(t)=Acos(wt+o)

Answer 9

yeas

Answer 10

use the chain rule

Answer 11

wait so I got \[x(t)=Acos((\sqrt{k/m} )t)\] is that what you guys got

Answer 12

yes