### 1. Characterizing Oscillations#### (a) The equation of motion for a particle undergoing simple harmonic motion is described with the following function: \( y(t) = (3.5 \text{ meters}) \sin (8.0 \pi t) \) where time is in units of seconds. What is the i. **Amplitude:** ii. **Period:** iii. **Frequency:** iv. **Angular frequency:**#### (b) Write the equation of motion for the graph:![Graph]**Graph Description:**The graph depicts a sine wave motion with time (\( t \)) on the horizontal axis and displacement (\( y(t) \)) on the vertical axis. The horizontal axis is labeled \( t(s) \) and spans from \( t = 0 \) to \( t = 8 \text{ seconds} \). The vertical axis is labeled \( y(t) \) ranging from \( +10 \text{ meters} \) to \( -10 \text{ meters} \).Key features of the graph:- The wave oscillates between \( +10 \text{ meters} \) and \( -10 \text{ meters} \).- The sine wave completes one full cycle (peak to peak) over a period of \( 4 \text{ seconds} \).- There are two complete cycles visible within the 8-second span.### Additional Information:#### Amplitude:The amplitude is the maximum displacement from the equilibrium position. From the equation \( y(t) = 3.5 \sin (8.0 \pi t) \), the amplitude is \( 3.5 \text{ meters} \).#### Period:The period is the time it takes for one complete cycle of the motion. Using the formula \( T = \frac{2\pi}{\omega} \), where \(\omega\) (angular frequency) is \( 8.0 \pi \), the period \( T \) is \( \frac{2\pi}{8.0\pi} = \frac{1}{4} \text{ seconds} \).#### Frequency:Frequency (\( f \)) is the number of cycles per second. Given the period \( T \) is \( \frac{1}{4} \text{ seconds} \), the frequency \( f \) is \( \frac{1}{T} =

1.a Given, Compare with this equation i. Amplitude of function is, A=3.5meters ii. The period is,…

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