Verified Solution • 2025–26 Session
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QNEET-2024-Ph-65: NEET 2024 Physics - Class 11 NEET-2024-Ph-65 Solution: If \(x = 5 ( t + { }{3})\ {m}\) represents the motion of a…
If represents the motion of a particle executing simple harmonic motion the amplitude and time period of motion respectively are 5 cm 2 s 5 m 2 s 5 cm 1 s 5 m 1 s
Multiple Choice Options
- A 5 cm, 2 s
- B 5 m, 2 s
- C 5 cm, 1 s
- D 5 m, 1 s
Step-by-Step Verified Solution
In the equation for simple harmonic motion (SHM), x = 5 sin _ ( � t + � 3 ) m , the general form x = A sin _ ( _ t + _ ) can be used to identify the parameters of SHM, where:
A is the amplitude.
_ (omega) is the angular frequency.
_ (phi) is the phase constant.
t is the time.
Comparing the given equation with the standard form:
The amplitude A is 5 m, as that is the coefficient of sine in the equation.
The angular frequency _ is � rad/s.
The angular frequency _ is related to the time period T of the motion through the formula:
_ = 2 � T .
Given that _ = � , we can substitute and solve for T :
� = 2 � T _ T = 2 � � = 2 seconds .
Hence, the amplitude of the motion is 5 m and the time period is 2 s. Thus, the correct answer is:
Option B: 5 m, 2 s