The initial position, velocity, and acceleration of an object moving in simple harmonic motion are xi’ vi’ and ai; the angular frequency of oscillation is ω. (a) Show that the position and velocity of the object for all time can be written as
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Automotive engineers refer to the time rate of change of acceleration as the "jerk". Assume an object moves in one dimension such that its jerk J is constant. Determine expressions for its
(a) acceleration,
(b) velocity,
(c) position,
given that its initial acceleration, velocity, and position are ai, vi, xi respectively.
In mechanics, an object whose position relative to a rest position is given by a generalized cosine or sine function.
Is called a simple harmonic oscillator. Examples of the simple harmonic oscillator are a mass suspended from a spring and a pendulum swinging through a small angle, in the absence of frictional damping forces. When we take damping forces into account, we obtain a damped harmonic oscillator:
A mass on a spring is undergoing simple harmonic motion so that its vertical position at time t seconds is given by
Cm below the rest position.
The frequency of oscillation is defined as the reciprocal of the period. What is the frequency of the oscillation of spring?
A pendulum makes 28 oscillations in exactly 50 s. What is its:
(a) Period?
(b) frequency?
(c) angular frequency?
An object with mass 2.7 kg is executing simple harmonic motion, attached to a spring with spring constant k = 310 N/m. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s.
(a) Calculate the angular speed
(b) Calculate the period
(c) If the motion amplitude was 5.5 cm, then calculate the maximum speed attained by the object.
