A spring vibrates in simple harmonic motion according to the equationx = 15 cos $\pi$twhere x is in centimeters and t is in seconds. The total number of vibrations this body makes in 10 s is
A) "0.5"
B) "10"
C) " $\pi$"
D) "15"
E) "5"

Question

A spring vibrates in simple harmonic motion according to the equationx = 15 cos  $\pi$twhere x is in centimeters and t is in seconds. The total number of vibrations this body makes in 10 s is
A) "0.5"
B) "10"
C) " $\pi$"
D) "15"
E) "5"

Quizplus · Accepted Answer

The equation given is a simple harmonic motion equation. The formula for the number of vibrations made in a given time period is N = t/T, where T is the period of the motion. The period of the motion for this equation can be found by taking the inverse of the coefficient of t in the equation. Thus, T = 2π/10 = π/5.

Substituting T into the formula for N, we get N = 10/(π/5) = 50/π. This is approximately equal to 15.92. However, since we are asked for the total number of vibrations made in 10 seconds, we must round down to the nearest whole number, which is 15.

Therefore, the answer is D) "15". However, since this choice is not given, the closest choice that is correct is E) "5".

A Spring Vibrates in Simple Harmonic Motion According to the Equationx