The tub is displaced 11cm from its equilibrium position of x = 0 and released at time t = 0.Ĭalculate the angular frequency, frequency and period of the motion. (ω is the angular frequency.)Ī tub of mass 650g is attached to a spring with spring constant 65 N/m. Where ε is the phase angle, a is the amplitude and n is the number of cycles in the period. Renaming the constant of integration as ε gives Since the maximum speed occurs when the particle is at the midpoint, The displacement is equal to the amplitude, a. Since simple harmonic motion is sinusoidal,įurther, when v = 0, the particle is at a maximum or minimum. The rate of change of angular displacement is called angular frequency.
The difference between the old and new angle is called angular Where n is the number of cycles in the period. Timing is started at the midpoint, with the particle headed towards P. If an object exhibits simple harmonic motion, a force must be acting on the object. Simple harmonic motion is accelerated motion. The following represents the displacement of the particle from the midpoint in the x direction as it bounces between the limits O and P. For simple harmonic motion, the acceleration a - 2 x is proportional to the displacement, but in the opposite direction. The particle's speed is greatest at the midpoint and zero at points O and P.
Speed is the magnitude of velocity, which is the rate of change of displacement with time. Simple harmonic motion is sinusoidal.Īs the particle moves from P to O and back again, its motion in the x direction can be graphed as a function of time : Simple harmonic motion occurs when the magnitude of the acceleration of the particle is proportional to the distance from the fixed point and acts in the opposite direction to the displacement.
The SI unit for frequency is the hertz (Hz), which is 1 oscillation per second. The frequency of the motion is the number of oscillations per second. Harmonic motion occurs when a particle undergoes oscillating or periodic motion.
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