Question

A particle executes SHM with a time period of 2s and amplitude 5 cm . Find (i) displacement (ii) velocity and (iii) acceleration, after 1/3 second; starting from the mean position. 

          A particle executes SHM with a time period of 2s and amplitude 5 cm . Find (i) displacement (ii) velocity and (iii) acceleration, after 1/3 second; starting from the mean position.

Added by Larry E.

University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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A particle executes SHM with a time period of 2s and amplitude 5 cm . Find (i) displacement (ii) velocity and (iii) acceleration, after 1/3 second; starting from the mean position.
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Transcript

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0:00 Hi there's a question.
00:01 It says that a particle executes shm that is simple harmonic motion with a time period of two seconds and amplitude five centimeters.
00:13 So if we draw simple simple harmonic motion this is time.
00:19 This is why.
00:21 So i can write simple harmonic motion in two ways.
00:25 This is one this is one way and this is the another way.
00:31 Anyhow, the period is going to be 2 pi but in this case we have period of simple harmonic motion as five seconds sorry two seconds and amplitude that is this value because this is the mean position and this is maximum so either this value or this value is known as the amplitude so amplitude is 5 centimeters and to find displacement velocity and acceleration of after 1 by 3 seconds.
01:07 So first of all i need to write i need to write okay i need to write equation of this shm so let us say shm is like a sign b t so this is simple s hm where a is amplitude and the period of this shm is 2 pi by b now if you look at the given information 2 pi by b is equal to 2 that is b will be equal to pi and a is amplitude which is 5 centimeters that means if you plug in in this y will be equal to 5 sine pi into t this is required equation for displacement of shton displacement of the wave okay so first of all i need to find displacement after 1 by 3 seconds.
02:17 Why when t equal to 1 by 3 will be 5 sine pi into 1 by 3...
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