The phase of SHM at time t is π/6.the following inference is drawn fro...
Let x = A sin (ω t + Ф)
Given ω t + Ф = π/6
So x = A /2
dx / dt = v = A ω cos (ω t + Ф) = A ω √3/2
Since x and y are positive, the particle is at x = A/2 and moving in +x direction.
This question is part of UPSC exam. View all Class 11 courses
The phase of SHM at time t is π/6.the following inference is drawn fro...
The Phase of SHM at Time t
The phase of Simple Harmonic Motion (SHM) at time t is given by the angle φ, which represents the position of the object undergoing SHM at that particular moment. In this case, the phase of SHM is given as π/6.
Understanding Simple Harmonic Motion:
Simple Harmonic Motion refers to the repetitive back-and-forth motion of an object around a mean or equilibrium position, where the restoring force is directly proportional to the displacement from the mean position and acts in the opposite direction.
Inference Drawn from the Phase of SHM at Time t:
1. Determining the Position:
The phase of SHM provides information about the position of the object undergoing the motion at a specific time t. By knowing the phase angle, one can determine the exact displacement from the mean position at that particular moment.
2. Relationship with Time:
The phase of SHM is directly related to time. As time progresses, the phase of the motion changes continuously, allowing us to track the position of the object at different moments in time.
3. Obtaining the Amplitude:
The phase of SHM alone does not provide information about the amplitude of the motion. The amplitude represents the maximum displacement of the object from the mean position. Therefore, to fully understand the motion, it is necessary to know the amplitude in addition to the phase.
4. Phase Difference and Frequency:
The phase difference between two objects undergoing SHM can determine their relative positions and the time it takes for one object to reach a certain position compared to the other. Additionally, the phase difference is related to the frequency of the motion. A phase difference of 2π (or 360 degrees) corresponds to one complete cycle of the motion, which is directly related to the frequency.
Conclusion:
The phase of SHM at time t provides crucial information about the position of the object undergoing the motion at that particular moment. It helps in understanding the relationship between time and position, determining the phase difference between multiple objects, and relating the phase to the frequency of the motion. However, to fully comprehend the motion, additional information such as the amplitude is required.
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.