Chapter: Oscillations and Waves
The time period of a 1 m long pendulum approximates to
A diagram depicting a simple pendulum, showing the length \( L \), the pivot point, and the path of the bob swinging, aiding in visualizing the concept of the oscillation and its time period.
Verified against NCERT Class XII Physics, Chapter 15 (Oscillations).
A simple pendulum having bob of mass m and length of string l has time period of T. If the mass of the bob is doubled and the length of the string is halved, then the time period of this pendulum will be
The time period \(T\) of a simple pendulum is given by the formula:
where \(l\) is the length of the pendulum and \(g\) is the acceleration due to gravity. Notably, the mass \(m\) of the bob does not affect the time period of the pendulum.
Initially, let the length be \(l\) and the time period be \(T\):
Now, the mass of the bob is doubled (\(2m\)) but does not impact \(T\). The length of the string is halved, so we now have:
The new time period \(T'\) becomes:
Simplifying this gives:
Thus, the new time period is \(\frac{T}{\sqrt{2}}\).
Remember, the mass of the pendulum does not affect the time period; only the length does. "Length down, period down but with a factor of \(\sqrt{2}\)."
Schematic diagram showing a simple pendulum with labeled length \(l\) and bob mass \(m\). Include two scenarios: the original pendulum and the modified pendulum (reduced length and increased mass).
Verified against standard physics textbooks and NCERT Class XI Physics, Chapter 15 (Oscillations).
Which one of the following statementsregarding simple pendulum is correct? Simple pendulum has a timeperiod independent of amplitude :
The time period \( T \) of a simple pendulum is governed by the formula:
where:
For small angular displacements, the gravitational force provides a restoring force proportional to displacement. Thus:
Using the small angle approximation, the equation of motion becomes:
For small amplitudes:
The restoring force is proportional to the displacement:
This leads to simple harmonic motion with a constant time period \( T \), independent of amplitude.
Remember: "For small swings, time rings are the same." This helps recall that small displacements yield constant periods.
A clean diagram of a simple pendulum, illustrating its length \( l \), amplitude \( A \), and angle \( \theta \) with the vertical. Include force vectors for gravity and tension to elucidate net force perpendicular to motion.
Verified against NCERT Class XI Physics, Chapter 15 (Oscillations).
The length of a simple pendulum is increased four times to its previous value while the mass is doubled. What is the ratio of the new and previous time period of the pendulum?
t:T 2:1📌 Hints / Properties Used:
📊 Visual Diagram Suggestion:
[A labeled diagram of a simple pendulum indicating the length and its properties, including a side-by-side comparison of the time periods before and after the change in length and mass]
Which one of the following statements is true for a simple harmonic oscillator?
A schematic diagram illustrating the position of a mass on a spring, showing the equilibrium position, maximum displacement, and the opposite direction of the restoring force relative to the displacement.
Verified against NCERT Class XI Physics, Chapter on Oscillations.
This is a preview of the SenaPrep Question Bank. To access comprehensive chapter-wise exercises, bookmark questions, attempt custom tests, and track your progress, download the official SenaPrep Android App.
Download Android App
SENAPREP