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A simple harmonic oscillator has an amplitude A and time period T. The time required by it to travel from x = A to x = A/2 is [1992]
- a)T/6
- b)T/4
- c)T/3
- d)T/2
Correct answer is option 'A'. Can you explain this answer?
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A simple harmonic oscillator has an amplitude A and time period T. The...
For S.H.M.,
When x = A, 
When
or, 
Now, time taken to travel from x = A to x = A/2 is (T/4 – T/12) = T/6
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A simple harmonic oscillator has an amplitude A and time period T. The...
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A simple harmonic oscillator has an amplitude A and time period T. The...
Time period of a simple harmonic oscillator is the time taken for one complete oscillation. It is denoted by T.
In one complete oscillation, the oscillator starts from one extreme position, goes to the other extreme position, and comes back to the starting position.
Given that the amplitude of the oscillator is A, the extreme positions are at x = +A and x = -A.
To find the time required for the oscillator to travel from x = A to x = A/2, we need to find the time taken for the oscillator to travel half of its amplitude.
Let's break down the solution into steps:
Step 1: Find the time taken for the oscillator to travel from x = 0 to x = A/2
Since the oscillator starts from x = 0, the time taken to travel from x = 0 to x = A/2 is half of the time period T/2.
Step 2: Find the time taken for the oscillator to travel from x = A/2 to x = A
Since the oscillator starts from x = A/2, the time taken to travel from x = A/2 to x = A is also half of the time period T/2.
Step 3: Add the times from Step 1 and Step 2
The total time taken for the oscillator to travel from x = 0 to x = A is T/2 + T/2 = T.
Step 4: Find the time taken for the oscillator to travel from x = A to x = A/2
Since the time taken for the oscillator to travel from x = 0 to x = A is T, the time taken for the oscillator to travel from x = A to x = A/2 is half of T, which is T/2.
Therefore, the correct answer is option (A) T/6.
In one complete oscillation, the oscillator starts from one extreme position, goes to the other extreme position, and comes back to the starting position.
Given that the amplitude of the oscillator is A, the extreme positions are at x = +A and x = -A.
To find the time required for the oscillator to travel from x = A to x = A/2, we need to find the time taken for the oscillator to travel half of its amplitude.
Let's break down the solution into steps:
Step 1: Find the time taken for the oscillator to travel from x = 0 to x = A/2
Since the oscillator starts from x = 0, the time taken to travel from x = 0 to x = A/2 is half of the time period T/2.
Step 2: Find the time taken for the oscillator to travel from x = A/2 to x = A
Since the oscillator starts from x = A/2, the time taken to travel from x = A/2 to x = A is also half of the time period T/2.
Step 3: Add the times from Step 1 and Step 2
The total time taken for the oscillator to travel from x = 0 to x = A is T/2 + T/2 = T.
Step 4: Find the time taken for the oscillator to travel from x = A to x = A/2
Since the time taken for the oscillator to travel from x = 0 to x = A is T, the time taken for the oscillator to travel from x = A to x = A/2 is half of T, which is T/2.
Therefore, the correct answer is option (A) T/6.
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