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wowolala
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Homework Statement
Let Z(t)=(5)Sin(2∏/3t) in SHO
guys, who knows how to find the Period T from above equation ?
thx
Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction of the displacement. This results in a motion that is repetitive and predictable.
Some common examples of SHM include a mass on a spring, a pendulum, and a swinging door. Other examples include the back-and-forth motion of a swing and the motion of a tuning fork.
The equation for SHM is x = A cos(ωt + φ), where x is the displacement from equilibrium, A is the amplitude (maximum displacement), ω is the angular frequency, and φ is the phase constant. This equation can also be written as x = A sin(ωt + φ) depending on the initial conditions of the motion.
The period of SHM is affected by the mass of the object, the stiffness of the restoring force (such as the spring constant), and the amplitude of the motion. The period is also inversely proportional to the square root of the gravitational acceleration, meaning that objects with larger masses will have longer periods.
Simple Harmonic Motion involves the transfer of energy between potential energy (stored energy) and kinetic energy (energy of motion). At the equilibrium point, all of the energy is in the form of potential energy, while at the maximum displacement, all of the energy is in the form of kinetic energy. This energy transfer continues as the object oscillates back and forth.