Which of the following with respect to a body performing simple harmonic motion are in phase?
displacement and velocity of the body
displacement and force on the body
velocity and acceleration of the body
force acting on the body and the acceleration
Explanation
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Discussions (16)
Option A is incorrect. Now, velocity is the rate of change of displacement, this means if the displacement is a sine function, differentiating it will give a cosine function which must be out of phase with the sine function by 90 degrees. So, velocity is out of phase with displacement, and leads it by 90degrees.
Option B is incorrect. displacement is not in phase with the force on the body because the force acting on the body will remain constant irrespective of the displacement provided damping and external air friction acting on the body is zero.
C is incorrect. Same thing is applicable to acceleration which is the rate of change of velocity. Hence, acceleration is out of phase with velocity by 90degrees.
D is the correct answer. force on the body is directly proportional to the acceleration of the body. If there are no external damping or air friction acting on the body, the force acting on it will remain constant. Same thing happens to the acceleration which is a constant called acceleration due to gravity.
D is the correct answer. force on the body is directly proportional to the acceleration of the body. If there are no external damping or air friction acting on the body, the force acting on it will remain constant. Same thing happens to the acceleration which is a constant called acceleration due to gravity.
More Explanation
Two things are said to be in phase if their wave form have the same frequency and are either both negative of both positive at a given time. For instance, two sine waves may have different amplitudes but if their wave lines cuts through the horizontal time-axis at the same points, they are said to be in phase. But if the two wave-lines cut through the time-axis at different points, they are said to be out of phase.
๐ข๐ฝ๐๐ถ๐ผ๐ป ๐ ๐ฎ๐ป๐ฑ ๐ ๐ฎ๐ฟ๐ฒ ๐ฐ๐ผ๐ฟ๐ฟ๐ฒ๐ฐ๐. ๐ง๐ต๐ฒ ๐ณ๐ผ๐ฟ๐ฐ๐ฒ ๐ฎ๐ป๐ฑ ๐ฎ๐ฐ๐ฐ๐ฒ๐น๐ฒ๐ฟ๐ฎ๐๐ถ๐ผ๐ป ๐๐ฎ๐ฟ๐ถ๐ฒ๐ ๐๐ถ๐๐ต ๐๐ต๐ฒ ๐ฑ๐ถ๐๐ฝ๐น๐ฎ๐ฐ๐ฒ๐บ๐ฒ๐ป๐, ๐ฎ๐๐๐ฎ๐ถ๐ป๐ถ๐ป๐ด ๐ฝ๐ฒ๐ฎ๐ธ ๐๐ฎ๐น๐๐ฒ๐ ๐๐ต๐ฒ๐ป ๐๐ต๐ฒ ๐ฑ๐ถ๐๐ฝ๐น๐ฎ๐ฐ๐ฒ๐บ๐ฒ๐ป๐ ๐ถ๐ ๐บ๐ฎ๐ ๐ถ๐บ๐๐บ. ๐ง๐ต๐ฒ ๐ณ๐ผ๐ฟ๐ฐ๐ฒ ๐ถ๐ ๐ฐ๐น๐ผ๐๐ฒ๐น๐ ๐ฟ๐ฒ๐น๐ฎ๐๐ฒ๐ฑ ๐๐ผ ๐๐ต๐ฒ ๐ฎ๐ฐ๐ฐ๐ฒ๐น๐ฒ๐ฟ๐ฎ๐๐ถ๐ผ๐ป (-๐บฯยฒ๐). ๐๐ฐ๐ฐ๐ฒ๐น๐ฒ๐ฟ๐ฎ๐๐ถ๐ผ๐ป, ๐ณ๐ผ๐ฟ๐ฐ๐ฒ ๐ฎ๐ป๐ฑ ๐ฑ๐ถ๐๐ฝ๐น๐ฎ๐ฐ๐ฒ๐บ๐ฒ๐ป๐ ๐ฎ๐ฟ๐ฒ ๐ถ๐ป ๐ฝ๐ต๐ฎ๐๐ฒ.
the correct answer is D. it can never be C because acceleration is out of phase with velocity by 90ยฐ
I think so is D because velocity has nothing to do with acceleration when it comes to phase. It should be force acting on it because increase in force weather damped or free increase acceleration
it cant be displacement bcos the acceleration of the force is un opposite direction to the displacement
Walai answer suppose be D
Two things are said to be in phase if their wave form have the same frequency and are either both negative of both positive at a given time. For instance, two sine waves may have different amplitudes but if their wave lines cuts through the horizontal time-axis at the same points, they are said to be in phase. But if the two wave-lines cut through the time-axis at different points, they are said to be out of phase.
