Question

find a model for simple harmonic motion if the position at t=0 is 0 the amplitude is 5 centimeters and the period is 4 seconds

Answer 1

Answer:

y = 5sin$(\frac{x}{2})$

Step-by-step explanation:

Since harmonic motion is represented by the sine wave equation.

y = a sin (bx)

where a = amplitude

period = $\frac{2\pi}{b}$

Amplitude of the harmonic motion is given as 5 and period is 4 seconds.

so a = 5

and 4 = $\frac{2\pi}{b}$ ⇒ b = $\frac{2\pi}{4}$

b = $\frac{\pi}{2}$

Now we replace the values of a and b in the sine equation

y = 5sin$(\frac{x}{2})$

Answer 2

d = 5sin(πt) 
hope this helped