Question

A mass $0.4\ \text{kg}$ performs S.H.M. with a frequency $\frac{16}{\pi}\ \text{Hz}$. At a certain displacement it has kinetic energy $2\ \text{J}$ and potential energy $1.2\ \text{J}$. The amplitude of oscillation is

• A. $0.15\ \text{m}$
• B. $0.125\ \text{m}$
• C. $0.075\ \text{m}$
• D. $0.1\ \text{m}$

Hint:

To simplify calculations with decimals under exam conditions, convert them into clean fractions! Writing $3.2 = \frac{16}{5}$, $m = \frac{2}{5}$, and $\frac{1}{2}m = \frac{1}{5}$ makes the equation become: $\frac{16}{5} = \frac{1}{5} \times 1024 \times A^2 \implies 16 = 1024 A^2 \implies A^2 = \frac{16}{1024} = \frac{1}{64}$. This completely removes multi-digit decimal division!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Simplify an equation containing decimals by converting all values into clean fractional forms to avoid multi-digit decimal arithmetic.

Step 2: Key Formula or Approach:
Convert each decimal to its exact fractional equivalent: 3.2 = 16/5, m = 2/5, and (1/2)m = 1/5. Substitute these into the given equation and solve algebraically.

Step 3: Detailed Explanation:
The equation becomes: 16/5 = (1/5) × 1024 × A². Multiplying both sides by 5 cancels the denominator completely: 16 = 1024 × A². Rearranging gives A² = 16/1024 = 1/64. Taking the square root yields A = 1/8. This fractional approach entirely eliminates the risk of decimal point errors during manual calculation.

Step 4: Final Answer:
The variable A² simplifies cleanly to 1/64.