Here are the essential concepts you must grasp in order to answer the question correctly.
Simple Harmonic Motion (SHM)
Simple Harmonic Motion describes the oscillatory motion of an object where the restoring force is directly proportional to the displacement from its equilibrium position. In this context, the mass on the spring exhibits SHM, characterized by sinusoidal functions for position and velocity, which can be analyzed to determine key parameters like period and amplitude.
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Period and Frequency
The period of a motion is the time taken for one complete cycle of oscillation, while frequency is the number of cycles per unit time. For SHM, the period (T) can be derived from the angular frequency (ω) using the relationship T = 2π/ω. In this case, the angular frequency is given as 4.71 rad/s, allowing for the calculation of the period.
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Maximum Acceleration and Force Constant
The maximum acceleration in SHM is given by the formula a_max = ω²A, where A is the amplitude of the motion. The force constant (k) of the spring relates to the mass (m) and angular frequency (ω) through the equation k = mω². Understanding these relationships is crucial for determining the maximum acceleration and the spring's force constant from the given parameters.
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