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In Physics / High School | 2014-06-30

A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with time according to the equation \(x = 0.5 \sin (\pi t + \frac{\pi}{3})\).

The acceleration (in \(\text{m/s}^2\)) of the body at \(t = 1.0\) s is approximately:

A. 3.5
B. 49
C. 14
D. 43
E. 4.3

Asked by Quincy851

Answer (2)

To find the acceleration at t = 1.0 s for a body oscillating with simple harmonic motion, differentiate the displacement equation twice with respect to time. Substitute the value of t into the acceleration equation to get the approximate value. None of the provided options are correct. ;

Answered by irma54 | 2024-06-18

The acceleration of the body oscillating with simple harmonic motion at t = 1.0 s is approximately 4.3 m/s². This value is derived by calculating the second derivative of the position function and evaluating it at t = 1.0 s. Therefore, the correct answer is option E, 4.3.
;

Answered by irma54 | 2024-09-30

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