A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is:
(a) 5 cm.
(b) 3 cm.
(c) 0 cm.
Answers
Answered by
0
ʀ = 5 ᴄᴍ = 0.05 ᴍ
ᴛ = 0.2 s
ω = 2π/ᴛ = 2π/0.2 = 10 π ʀᴀᴅ/s
ᴡʜᴇɴ ᴅɪsᴘʟᴀᴄᴇᴍᴇɴᴛ ɪs ʏ, ᴛʜᴇɴ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ, ᴀ = -ω2ʏ
ᴄᴀsᴇ (ᴀ) ᴡʜᴇɴ ʏ = 5ᴄᴍ = 0.05 ᴍ
ᴀ = -(10π)2 × 0.05 = -5π2 ᴍ/s2
ᴄᴀsᴇ (ʙ) ᴡʜᴇɴ ʏ = 3 ᴄᴍ = 0.03 ᴍ
ᴀ = -(10π)2 × 0.03 = -3π2 ᴍ/s2
ᴄᴀsᴇ (ᴄ) ᴡʜᴇɴ ʏ = 0
ᴀ = -(10π)2 × 0 = 0
answer is 5cm option a
ᴛ = 0.2 s
ω = 2π/ᴛ = 2π/0.2 = 10 π ʀᴀᴅ/s
ᴡʜᴇɴ ᴅɪsᴘʟᴀᴄᴇᴍᴇɴᴛ ɪs ʏ, ᴛʜᴇɴ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ, ᴀ = -ω2ʏ
ᴄᴀsᴇ (ᴀ) ᴡʜᴇɴ ʏ = 5ᴄᴍ = 0.05 ᴍ
ᴀ = -(10π)2 × 0.05 = -5π2 ᴍ/s2
ᴄᴀsᴇ (ʙ) ᴡʜᴇɴ ʏ = 3 ᴄᴍ = 0.03 ᴍ
ᴀ = -(10π)2 × 0.03 = -3π2 ᴍ/s2
ᴄᴀsᴇ (ᴄ) ᴡʜᴇɴ ʏ = 0
ᴀ = -(10π)2 × 0 = 0
answer is 5cm option a
Similar questions