# Math Help - 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
$d$ is a sinusoidal function of $t$; i.e. $d = a + b\sin(ct+d)$, for some constants $a, b, c, d$

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

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

$\Rightarrow a=80, b= 30$

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

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

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

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

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

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

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