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A body is executing simple harmonic motion. When the displacements from the mean position are 4 cm and 5 cm, the corresponding velocities of the body are 10 cm s⁻¹ and 8 cm s⁻¹. Then the time period of the body is

Asked in CBSE AIPMT 1991 · v-x and a-x relations

• (1) 2π s
• (2) π/2 s
• (3) π s
• (4) (3π)/2 s

Step-by-step solution

Why the other options are wrong

• (1) 2π s needs ω=1 rad s⁻¹; subtracting the two velocity equations fixes ω²=(100-64)/(25-16)=4 s⁻²
• (2) comes from using ω²=4 in place of ω=2: T=(2π)/4=π/2
• (4) (3π)/2 s needs ω=4/3 rad s⁻¹, which no combination of the four given numbers produces

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