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The maximum speed and acceleration of a particle executing simple harmonic motion are 10 cm s-1 and 50 cm s-2. Find the position(s) of the particle when the speed is 8 cm s-1.

The maximum speed and acceleration of a particle executing simple harmonic motion are 10 cm s-1 and 50 cm s-2. Find the position(s) of the particle when the speed is 8 cm s-1.

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
Sol. vmax = 10 cm/sec. ⇒ rω = 10 ⇒ ω2 = 100/r2 ….(1) Amax = ω2r = 50 cm/sec ⇒ ω2 = 50/y = 50/r …..(2) ∴ 100/r2 = 50/r ⇒ r = 2 cm. ∴ ω = √(100/r^2 ) = 5 sec2 Again, to find out the positions where the speed is 8m/sec, v2 = ω2 (r2 – y2) ⇒ 64 = 25 ( 4 – y2) ⇒ 4 – y2 = 64/25 ⇒ y2 = 1.44 ⇒ y = √1.44 ⇒ y = ± 1.2 cm from mean position.

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