Answer:
[tex]x = -1.437 cm[/tex]
Explanation:
The general equation for position of Simple harmonic motion is given as:
[tex]x = A sin(\omega t)[/tex] ........(1)
where,
x = Position of the wave
A = Amplitude of the wave
ω = Angular velocity
t = time
In this case, the amplitude is just half the range,
thus,
[tex]A =\frac{3cm}{2}=1.5cm[/tex] (Given range = 3cm)
A = 1.5 cm
Now, The angular velocity is given as:
[tex]\omega=\frac{2\pi}{T}[/tex]
Where, T = time period of the wave =0.27s (given)
[tex]\omega=\frac{2\pi}{0.27s}[/tex]
or
[tex]\omega=23.27s^{-1}[/tex]
so, at time t = 55 s, the equation (1) becomes as:
[tex]x = 1.5 sin(23.27\times 55)[/tex]
on solving the above equation we get,
[tex]x = -1.437 cm[/tex]
here the negative sign depicts the position in the opposite direction of +x
