A particle is suspended from a vertical spring which is executing S.H.M. of | PGMN Solutions

A particle is suspended from a vertical spring which is executing S.H.M. of frequency 5 Hz. The spring is unstretched at the highest point of oscillation. Maximum speed of the particle is (g = 10 m/s²).

Options:
(A) 1/π m/s
(B) 1/4π m/s
(C) 1/2π m/s
(D) π m/s



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🚀 Step-by-Step Solution to Solve This Question 🚀
📌 Chapter: Oscillations
📌 Topic: Simple Harmonic Motion (SHM) in Vertical Springs

🔹 Step 1: Understand the scenario
A particle hangs from a vertical spring, oscillating up and down in SHM with a frequency of 5 Hz. The spring is unstretched at the highest point, meaning no force is acting on it there.

🔹 Step 2: Relate SHM to the spring system
In SHM, the equilibrium position is where the spring force balances gravity. The amplitude is the maximum displacement from equilibrium. Here, the highest point (unstretched spring) is one amplitude above equilibrium.

🔹 Step 3: Find amplitude and angular frequency
At equilibrium, the spring stretches due to gravity. Using SHM properties, the angular frequency is calculated from the given frequency. The amplitude equals the stretch at equilibrium.

🔹 Step 4: Calculate maximum speed
In SHM, maximum speed occurs at equilibrium and depends on amplitude and angular frequency. Plugging in the values gives the answer.

✅ Final Answer: (A) 1/π m/s 🚀
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