Physics · No topic

To find the maximum acceleration of the projection executing simple harmonic motion on the horizontal diameter, we first recognize that this maximum acceleration (a_max) is given by the formula a_max = ω² * A, where ω is the angular velocity and A is the amplitude. In uniform circular motion, the linear velocity (v) is related to the angular velocity (ω) by the equation v = ω * r. Here, r is the radius (4 cm) and v is the linear velocity (4 cm/s). Therefore, we calculate ω as follows: ω = v/r = 4 cm/s / 4 cm = 1 rad/s. The amplitude A is equal to the radius, which is 4 cm. Now, substituting these values into the formula gives us a_max = (1 rad/s)² * 4 cm = 4 cm/s². Thus, the correct answer is 4 cm/s². The other options do not fit the derived formula and calculations.

This is the correct answer. The maximum acceleration is derived from the formula for centripetal acceleration in circular motion.

This value is double the correct answer but does not correspond to any known relationship in circular motion related to the parameters provided.

This option does not fit the calculations for maximum acceleration derived from the given velocity and radius.

This value is significantly higher than what would be expected based on the motion parameters provided, making it incorrect.