The acceleration of a body executing simple harmonic motion is maximum at
- A.The mean position
- B.The extreme positions
- C.One fourth of the amplitude
- D.It is constant throughout
Correct answer
Explanation
The correct answer is B, the extreme positions. In simple harmonic motion the acceleration equals minus omega squared times the displacement, so it grows with displacement and is greatest at the ends of the path, where its value is A omega squared and it points back towards the centre. Option A is wrong because at the mean position the displacement is zero, so the acceleration is zero even though the speed is at its maximum there. Option C is wrong because no special maximum occurs at one fourth of the amplitude. Option D is wrong because acceleration in simple harmonic motion is never constant; a constant acceleration, as in free fall, does not produce oscillation at all. The pairing to memorise is: velocity maximum at the mean position, acceleration maximum at the extremes.
Read the full article: Oscillations: Simple Harmonic Motion and Pendulum Notes
Practice Questions
View allIf a particle is moving with simple harmonic motion, the velocity is _________ at the mean position.
- A.Maximum
- B.Zero
- C.Minimum
- D.None of these
Show answer
In simple harmonic motion the velocity is given by omega times the square root of A squared minus x squared.
Read the full explanation →A child is sitting on a swing. Its minimum and maximum heights from the ground are 0.75 m and 2 m respectively. Its maximum speed will be
- A.10 m/s
- B.5 m/s
- C.8 m/s
- D.15 m/s
Show answer
A swing is a pendulum, and its speed is greatest at the lowest point, where all the potential energy gained at the top has turned into kinetic energy.
Read the full explanation →The time period of a simple pendulum does not depend on which of the following?
- A.The length of the pendulum
- B.The mass of the bob
- C.The acceleration due to gravity
- D.All of these
Show answer
The time period of a simple pendulum is two pi times the square root of the length divided by g, in which the mass of the bob does not appear at all; a heavy bob and a light bob of the same length keep the same time, which is the…
Read the full explanation →The length of a second's pendulum, at a place where the acceleration due to gravity is 9.8 m/s squared, is nearly
- A.1 metre
- B.2 metres
- C.0.5 metre
- D.9.8 metres
Show answer
A second's pendulum is one whose time period is exactly two seconds, so that each swing from one side to the other takes one second.
Read the full explanation →If the length of a simple pendulum is made four times its original value, its time period will become
- A.Four times
- B.Two times
- C.Half
- D.One fourth
Show answer
The time period varies as the square root of the length, so multiplying the length by four multiplies the period by the square root of four, that is by two; to double the period of a pendulum its length must be made four times.
Read the full explanation →