The maximum velocity of the mass can be found using the conservation of energy principle. The total energy in a simple harmonic motion is constant and is the sum of kinetic and potential energy.

The total energy E is given by:

E = 1/2 * k * A^2

where k is the spring constant and A is the amplitude of the motion.

Given that k = 9.00 N/m and the initial displacement A = 4.00 cm = 0.04 m, we can substitute these values into the equation to find E:

E = 1/2 * 9.00 N/m * (0.04 m)^2 = 0.0072 J

At the point of maximum velocity, all the energy is kinetic energy, which is given by:

E = 1/2 * m * v_max^2

where m is the mass and v_max is the maximum velocity. We can rearrange this equation to solve for v_max:

v_max = sqrt((2 * E) / m)

Substituting the given mass m = 4.00 kg and the calculated total energy E = 0.0072 J, we find:

v_max = sqrt((2 * 0.0072 J) / 4.00 kg) = 0.03 m/s

So, the maximum velocity of the mass is 0.03 m/s.

Question

The maximum velocity of the mass can be found using the conservation of energy principle. The total energy in a simple harmonic motion is constant and is the sum of kinetic and potential energy.

The total energy E is given by:

E = 1/2 * k * A^2

where k is the spring constant and A is the amplitude of the motion.

Given that k = 9.00 N/m and the initial displacement A = 4.00 cm = 0.04 m, we can substitute these values into the equation to find E:

E = 1/2 * 9.00 N/m * (0.04 m)^2 = 0.0072 J

At the point of maximum velocity, all the energy is kinetic energy, which is given by:

E = 1/2 * m * v_max^2

where m is the mass and v_max is the maximum velocity. We can rearrange this equation to solve for v_max:

v_max = sqrt((2 * E) / m)

Substituting the given mass m = 4.00 kg and the calculated total energy E = 0.0072 J, we find:

v_max = sqrt((2 * 0.0072 J) / 4.00 kg) = 0.03 m/s

So, the maximum velocity of the mass is 0.03 m/s.

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