# Simple harmonic motion problem

• ryanuser
In summary, the conversation discussed a problem involving a body performing simple harmonic motion with a given displacement equation. The question was to find the frequency of the oscillation, with multiple choice answers provided. The correct answer according to the mark scheme is B, but some confusion arose as to whether the answer should be B or C based on different formulas used. It was noted that choosing answer B may have been a trap for those who were in a hurry and calculated the time period first.
ryanuser

## Homework Statement

A body performaning simple harmonic motion has a displacement x given by the equation x= 30 sin 50t, where t is the time in seconds. what is the frequency of the oscillation?
A. 0.020Hz B. 0.13Hz C. 8.0Hz D. 30Hz E. 50Hz
(correct answer is B according to the mark scheme)

## Homework Equations

ω = 2πf
x = Amplitude cos (2πf t)
x = Amplitude sin (2πf t)
x = Amplitude cos (ω t)
x = Amplitude cos (ω t)

## The Attempt at a Solution

f = 50/2π = 7.9577Ηz according to the standard SHM formulas, which means the answer is C not B? what has gone wrong?

ryanuser said:
f = 50/2π = 7.9577Ηz according to the standard SHM formulas, which means the answer is C not B? what has gone wrong?
I'd say you are correct.

Interestingly, answer B is the inverse of that (1/f).

Sahil Kukreja
Doc Al said:
I'd say you are correct.

Interestingly, answer B is the inverse of that (1/f).

those who had calculated time period first and were in a hurry would mark (B) in the exam

Sahil Kukreja said:
those who had calculated time period first and were in a hurry would mark (B) in the exam
Exactly. It's a trap!

## 1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object moves back and forth in a straight line with a constant frequency. This motion occurs when the restoring force on the object is directly proportional to its displacement from equilibrium.

## 2. What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A sin(ωt + φ), where x is the displacement of the object, A is the amplitude, ω is the angular frequency, and φ is the phase angle.

## 3. How do you determine the period of a simple harmonic motion?

The period of a simple harmonic motion can be determined by taking the inverse of the frequency, which is given by f = ω/2π. Therefore, the period can be calculated as T = 1/f = 2π/ω.

## 4. How does amplitude affect simple harmonic motion?

The amplitude of a simple harmonic motion determines the maximum displacement of the object from equilibrium. A larger amplitude results in a greater maximum displacement and a longer period of motion.

## 5. What factors can affect the frequency of simple harmonic motion?

The frequency of simple harmonic motion is affected by the mass of the object, the spring constant of the system, and the amplitude of the motion. A greater mass or higher spring constant will result in a lower frequency, while a larger amplitude will result in a higher frequency.

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