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2. (a) The equation of motion of a particle P moving in a straight line OX is dr + 6 + 4z = 0, where ris the displacement of P from O at time t. (de") dt Initially, Pis at O, moving with speed /āms Show that the displacement z of P can be written in the form I= Ae "cos(nt + e). stating the values of A, n and e (i) (ii) Find the period of the motion.

2. (a) The equation of motion of a particle P moving in a straight line OX is dr + 6 + 4z = 0, where ris the displacement of P from O at time t. (de") dt Initially, Pis at O, moving with speed /āms Show that the displacement z of P can be written in the form I= Ae "cos(nt + e). stating the values of A, n and e (i) (ii) Find the period of the motion.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. (a) The equation of motion of a particle P moving in a straight line OX is dr + 6 + 4z = 0, where ris the displacement of P from O at time t. (dt) dt Initially, Pis at O, moving with specd V3ms . (i) Show that the displacement r of Pcan be written in the form I = Ac "cos(nt + €). stating the values of A, n and e (ii) Find the period of the motion. (b) A particle performs simple harmonic motion with centre O and amplitude 2 metres. The period of oscillation is a seconds. P and Q are two points which lie at a distance V3m on either side of O. Find the time taken by the particle to move directly from P to Q.
Transcribed Image Text:2. (a) The equation of motion of a particle P moving in a straight line OX is dr + 6 + 4z = 0, where ris the displacement of P from O at time t. (dt) dt Initially, Pis at O, moving with specd V3ms . (i) Show that the displacement r of Pcan be written in the form I = Ac "cos(nt + €). stating the values of A, n and e (ii) Find the period of the motion. (b) A particle performs simple harmonic motion with centre O and amplitude 2 metres. The period of oscillation is a seconds. P and Q are two points which lie at a distance V3m on either side of O. Find the time taken by the particle to move directly from P to Q.
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