Question

For the simple harmonic motion described by the trig functioon, find (a) the maximum displacement, (b) the frequency, (c) the value of d when t = 5, and (d)) the least positive value of t for which d = 0.

d= 1/64 sin792 π t

Answer 1

@ybarrap

Answer 2

The maximum displacement is simply the amplitude of d.

The frequency can be found from the relation \(\omega=2\pi f\implies f=\cfrac{\omega}{2\pi}\). From d, \(\omega=792\pi\). Now just solve for \(f\), in hertz.

To find the value of d at \(t=5\), just plug into d.

When d=0, the sine value is zero. For what value of t is sine=0. If zero is excluded, the smallest positive value is when \(792\pi t=2\pi\). Now just solve for t.

Answer 3

so for (a) the answer is 1/64?

Answer 4

(b) is 1/64?

Answer 5

a is right
b is wrong, should be 792/2

Answer 6

alright, so for b it would be 792/2= 396?

Answer 7

make sense?

Answer 8

its 396 for (b), right?

Answer 9

792/2, whatever that is

Answer 10

alrighty.

Answer 11

For c what do u mean by pluggin it in.

Answer 12

$$
d= \left (1/64 \right )\sin(792 π (5))
$$

Answer 13

I get 6.125^-12 on calculator...

Answer 14

That's a pretty small number, might as well be zero:
\(792\times 5\) is a multiple of \(2\) and \(\sin(2n\pi)=0\) for \(n\in\mathbb N\)

Answer 15

so for (c) the answer is 0?