Shortcut Methods

Typical Numerical Problems on Simple Harmonic Motion For JEE Exam:

  1. Problem: A mass of 0.5 kg is attached to a spring with a spring constant of 100 N/m. Find the period and frequency of oscillation. Solution:

    • Period (T) = 2π0.5kg100N/m=0.63s
    • Frequency (f) = 10.63s=1.59Hz

  2. Problem: A spring-mass system has a mass of 2 kg and a spring constant of 200 N/m. If the system is displaced from its equilibrium position by 10 cm and released, find the amplitude and energy of oscillation. Solution:

    • Amplitude (A) = 0.1m2=0.071m
    • Energy (E) = 12⋅200N/m⋅(0.071m)2=0.504J

For CBSE Board Exam:

  1. Problem: A simple pendulum has a length of 1 m. What is the time period of oscillation of the pendulum? Solution:

    • Time Period (T) = 2π1m9.81m/s2=2.01s

  2. Problem: A mass of 0.2 kg is attached to a vertical spring with a spring constant of 50 N/m. If the mass is pulled down 5 cm from its equilibrium position and released, find the amplitude and frequency of oscillation. Solution:

    • Amplitude (A) = 0.05m=0.05m
    • Frequency (f) = 12π50N/m0.2kg=1.13Hz
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