Q.23 Physics · Section A ⭐ 360° Option Elimination Active

NEET 2024 Physics Question 23 Solution

Topic: Oscillations · Official NTA Booklet Code T1

Question

If x = 5 sin(πt + π/3) m represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are:

✓

Verified Against NTA Final Answer Key

Option (4) : 5 m, 2 s

📚 Oscillations Easy

📋 Given Parameters & Problem Setup

Equation of motion x = 5 sin(πt + π/3) m

Unit of displacement Meters (m)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Standard Form Direct Readout

⏱️ Save ~40 seconds

Compare x = A sin(ωt + φ): Amplitude A = 5 m; ω = π rad/s -> T = 2π/ω = 2π/π = 2 s -> (5 m, 2 s)!

1 Standard equation of SHM: x = A sin(ωt + φ).

2 Read off Amplitude: A = 5 m (watch out for cm traps!).

3 Read off Angular frequency: ω = π rad/s.

4 Time period: T = 2π / ω = 2π / π = 2 s.

5 Result: Amplitude = 5 m, Time period = 2 s -> Option (4) in 5 seconds!

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Why You Can 100% Trust This Shortcut: Fundamental Kinematics of Simple Harmonic Motion (x = A sin(ωt + φ) and T = 2π/ω).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Standard Equation of Simple Harmonic Motion

The general displacement equation of a particle executing simple harmonic motion (SHM) along the x-axis is given by:

x(t) = A \sin(\omega t + \phi)

Step 2

Direct Comparison and Amplitude Extraction

Comparing the given equation x = 5 sin(πt + π/3) m with the standard form: - Amplitude A = 5 m - Angular frequency ω = π rad/s - Initial phase angle φ = π/3 rad

A = 5\,\text{m}, \quad \omega = \pi\,\text{rad/s}

Step 3

Calculation of Time Period T

The time period T for one complete oscillation is related to the angular frequency ω by:

T = \frac{2\pi}{\omega} = \frac{2\pi}{\pi\,\text{rad/s}} = 2\,\text{s}

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 (1)

✗ Incorrect

Verdict & Scientific Reason:

Unit of amplitude is meters (m), not cm; period is 2 s, not 1 s.

⚠️

Student Fallacy (Why candidates pick this trap): Misreading meters as centimeters and calculating T = 1/ω = 1 s.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Calculates period as 1 s instead of 2 s.

⚠️

Student Fallacy (Why candidates pick this trap): Using T = π/ω instead of 2π/ω.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Amplitude unit error: writes 5 cm instead of 5 m.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming default textbook problems use cm.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Exact identification: Amplitude = 5 m, Time period = 2 s.

💡

Why this is airtight: None.

⚠️

NTA Trap Alert: Unit Trap: Meters vs Centimeters

Options (1) and (3) set a trap with "5 cm" because students frequently skim past the unit "m" printed outside the bracket.

🛡️ How to avoid the -1 mark: Notice that "m" is explicitly printed as the SI unit in the equation: x = 5 sin(πt + π/3) m.

📖

Core NEET Syllabus Standard

Physics Core Oscillations · Oscillations Standard Benchmark

Core Scientific Principle Tested:

"In x = A sin(ωt + φ), A is the amplitude, ω is the angular frequency, and the period is T = 2π/ω."

Syllabus Focus: Simple Harmonic Motion and Uniform Circular Motion

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Amplitude is upfront (5 m); Divide 2π by π to get 2 seconds!

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NEET 2024 Physics Question 23 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Standard Form Direct Readout

Step-by-Step Rigorous Workflow & Mathematical Proof

Standard Equation of Simple Harmonic Motion

Direct Comparison and Amplitude Extraction

Calculation of Time Period T

360° Option Elimination Engine Key Feature

NTA Trap Alert: Unit Trap: Meters vs Centimeters

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Oscillations

Time Period of a Floating Cylindrical Cork in Liquids of Different Densities

Condition for a Circular Phase Space Trajectory in Simple Harmonic Motion

Spring-Mass System with Slowly Leaking Mass (Variable Mass SHM)

Ratio of Amplitudes for Identical Masses with Equal Maximum Speeds

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