Final answer:
In simple harmonic motion, the maximum speed and acceleration are related to the amplitude. Without the angular frequency value, the amplitude cannot be calculated.
Step-by-step explanation:
In simple harmonic motion (SHM), the maximum speed and maximum acceleration are related to the amplitude of the motion. The maximum speed occurs when the object passes through the equilibrium position, and it is equal to the product of the angular frequency (ω) and the amplitude (A). In this case, the maximum speed is given as 4.3 m/s. So, we can write the equation as:
vmax = ωA
Similarly, the maximum acceleration in SHM is equal to the product of the angular frequency (ω) squared and the amplitude (A). In this case, the maximum acceleration is given as 0.65 m/s². So, we can write the equation as:
amax = ω²A
To find the amplitude (A), we can use the equations:
A = vmax / ω
A = amax / ω²
By substituting the given values, we can calculate the amplitude:
A = 4.3 m/s / ω
A = 0.65 m/s² / ω²
However, without the value of the angular frequency (ω), we cannot calculate the amplitude. Additional information would be necessary to solve for the amplitude in this case.