The position of air cart at is .
Explanation:
It is given that the air track cart completes one oscillation for simple harmonic motion (SHM) in every .
Initially at time at position the cart is released.
Our aim is to obtain the position of air track cart for time .
The function of time can be called as displacement. Since, this is a periodic motion the function of time will be periodic in nature.
The expression for simple periodic function is shown below.
......(1)
Here, is the amplitude for the maximum periodic function at time and is the angular frequency and is time in seconds.
It is given that initially at time the position is , so the amplitude of the function A is .
The angular frequency is an integral multiple of radians so, its value can be obtained as,
Substitute for in above equation to obtain the angular frequency as follows:
Substitute for , for and for in equation (1) to obtain the value of position.
Therefore, the displacement at time is .
Thus, the position of air cart at is .
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Oscillations
Keywords:
Air track, cart, spring, attached, oscillation, simple, harmonic, motion, position, released, time period, angular frequency, argument, periodic, displacement, amplitude, SHM.