Amplitude of SHM

The equation of motion for a particle executing simple harmonic motion (SHM) along the y-axis is given by:

y = A sin(ωt + φ)

where:
- y is the displacement of the particle at time t
- A is the amplitude of the SHM
- ω is the angular frequency of the SHM
- φ is the phase constant

In this case, the equation of motion is given as:

y = 2 10sin5πt

To determine the amplitude of the SHM, we need to compare it with the general equation of motion.

Comparison with the General Equation

Comparing the given equation with the general equation of motion, we can see that:
- The amplitude A is equal to 2 10.
- The angular frequency ω is equal to 5π.
- The phase constant φ is not provided in the given equation.

Interpreting the Amplitude

The amplitude of SHM represents the maximum displacement of the particle from its equilibrium position. In this case, the amplitude is given as 2 10. Since the amplitude is positive, the particle oscillates between a maximum displacement of +2 10 and a minimum displacement of -2 10.

The amplitude also provides information about the energy of the system. The total mechanical energy (E) of the SHM system is given by:

E = (1/2) mω²A²

where m is the mass of the particle. The greater the amplitude, the greater the energy of the system.

Summary

In summary, the amplitude of the SHM in this case is 2 10. It represents the maximum displacement of the particle from its equilibrium position and provides information about the energy of the system.

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