The maximum acceleration of the mass can be found using the equation for the acceleration of a simple harmonic oscillator, which is a = -ω²x.

In this case, ω is the angular frequency, and x is the displacement.

The angular frequency ω can be found using the equation ω = sqrt(k/m), where k is the spring constant and m is the mass.

Substituting the given values, we get ω = sqrt(9.00 N/m / 2.00 kg) = 2.12 rad/s.

The displacement x can be found from the velocity function v(t) = (10.0 cm/s) sin(ω t). The maximum velocity occurs when sin(ω t) = 1, so the maximum displacement x_max = v_max / ω = 10.0 cm/s / 2.12 rad/s = 0.0472 m.

Substituting these values into the equation for acceleration, we get a_max = -ω²x_max = -(2.12 rad/s)² * 0.0472 m = -0.212 m/s².

Therefore, the maximum acceleration of the mass is 0.212 m/s².

Question

The maximum acceleration of the mass can be found using the equation for the acceleration of a simple harmonic oscillator, which is a = -ω²x.

In this case, ω is the angular frequency, and x is the displacement.

The angular frequency ω can be found using the equation ω = sqrt(k/m), where k is the spring constant and m is the mass.

Substituting the given values, we get ω = sqrt(9.00 N/m / 2.00 kg) = 2.12 rad/s.

The displacement x can be found from the velocity function v(t) = (10.0 cm/s) sin(ω t). The maximum velocity occurs when sin(ω t) = 1, so the maximum displacement x_max = v_max / ω = 10.0 cm/s / 2.12 rad/s = 0.0472 m.

Substituting these values into the equation for acceleration, we get a_max = -ω²x_max = -(2.12 rad/s)² * 0.0472 m = -0.212 m/s².

Therefore, the maximum acceleration of the mass is 0.212 m/s².

Knowee AI · Accepted Answer

The maximum acceleration of the mass can be found using the equation for the acceleration of a simple harmonic oscillator, which is a = -ω²x.

In this case, ω is the angular frequency, and x is the displacement.

The angular frequency ω can be found using the equation ω = sqrt(k/m), where k is the spring constant and m is the mass.

Substituting the given values, we get ω = sqrt(9.00 N/m / 2.00 kg) = 2.12 rad/s.

The displacement x can be found from the velocity function v(t) = (10.0 cm/s) sin(ω t). The maximum velocity occurs when sin(ω t) = 1, so the maximum displacement x_max = v_max / ω = 10.0 cm/s / 2.12 rad/s = 0.0472 m.

Substituting these values into the equation for acceleration, we get a_max = -ω²x_max = -(2.12 rad/s)² * 0.0472 m = -0.212 m/s².

Therefore, the maximum acceleration of the mass is 0.212 m/s².

A 2.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. The velocity is given by the expression v(t) = (10.0 cm/s) sin(ω t). What is the maximum acceleration of the mass?

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