Well, Amplitude (A) is the maximum displacement from the equilibrium position. In this case, we can use the maximum speed (v_max) to find the amplitude.
Now, you're probably wondering how to relate speed to displacement in simple harmonic motion? Well, let me spring into action and explain!
In simple harmonic motion, the maximum speed occurs when the object is at the equilibrium position and all the potential energy stored in the spring is converted to kinetic energy.
The potential energy stored in the spring (PE_spring) is given by the equation PE_spring = (1/2) * k * A^2, where k is the spring constant and A is the amplitude.
And the kinetic energy (KE) of the object is given by the equation KE = (1/2) * m * v_max^2, where m is the mass of the object and v_max is the maximum speed.
Since the maximum speed occurs at the equilibrium position where the displacement is zero, the potential energy is also zero. Therefore, we can set PE_spring = 0.
Now we can equate the potential energy to the kinetic energy to express A in terms of v_max:
(1/2) * k * A^2 = (1/2) * m * v_max^2
Plugging in the given values, we have:
(1/2) * 120 N/m * A^2 = (1/2) * 0.20 kg * (2.0 m/s)^2
After some calculations, we can solve for the amplitude A. Hmm, let me do some math magic here... *abracadabra*
A = sqrt((0.20 kg * (2.0 m/s)^2) / 120 N/m)
*calculating, calculating...*
A ≈ 0.127 m
So, the amplitude of the motion is approximately 0.127 meters. Tada!