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Amit Saxena Grade: upto college level
        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.
3 years ago

Answers : (1)

Navjyot Kalra
askIITians Faculty
654 Points
										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.
3 years ago
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