# Thread: Don't get this pendelum problem??

1. ## Don't get this pendelum problem??

how the heck do i find the equation?? i dont get it!! i just need help with the equation then i can do the rest

2. Hello elpermic
Originally Posted by elpermic

how the heck do i find the equation?? i dont get it!! i just need help with the equation then i can do the rest
$\displaystyle d$ is a sinusoidal function of $\displaystyle t$; i.e. $\displaystyle d = a + b\sin(ct+d)$, for some constants $\displaystyle a, b, c, d$

$\displaystyle d_{max}=110\Rightarrow 110 = a+b$, since the maximum value of the sine function is $\displaystyle 1$

$\displaystyle d_{min}=50 =a-b$, since the minimum value of the sine function is $\displaystyle -1$

$\displaystyle \Rightarrow a=80, b= 30$

So $\displaystyle d = 80+30\sin(ct+d)$

$\displaystyle \sin(ct+d)$ has period $\displaystyle \frac{2\pi}{c}\Rightarrow \frac{2\pi}{c}= 6$, since the pendulum performs one complete swing in $\displaystyle 6$ seconds

$\displaystyle \Rightarrow c = \frac{\pi}{3}$

And $\displaystyle d = 110$ when $\displaystyle t = 1.3\Rightarrow \sin\Big(\frac{1.3\pi}{3}+d\Big) = 1$

$\displaystyle \Rightarrow \frac{1.3\pi}{3}+d = \frac{\pi}{2}$

$\displaystyle \Rightarrow d = \pi\Big(\frac{1}{2}-\frac{13}{30}\Big)=\frac{\pi}{15}$

$\displaystyle \Rightarrow d =80+30\sin\Big(\frac{\pi t}{3}+\frac{\pi}{15}\Big)$