Question

An object with mass 2.9 kg is executing simple harmonic motion, attached to a spring with spring constant 330 n/m . when the object is 0.025 m from its equilibrium position, it is moving with a speed of 0.65 m/s .

Calculate the amplitude of the motion.

Answer 1

The amplitude of the motion is approximately 0.11 meters.

Step-by-step explanation:

To calculate the amplitude of the motion, we can use the equation for the speed of an object in simple harmonic motion: v = ωA, where v is the speed, ω is the angular frequency, and A is the amplitude. Rearranging the equation, we get A = v/ω. We can find ω using the equation ω = √(k/m), where k is the spring constant and m is the mass. Plugging in the given values, we get ω = √(330 N/m / 2.9 kg) = 6.13 rad/s. Plugging in the values for v and ω, we get A = 0.65 m/s / 6.13 rad/s ≈ 0.11 m.