I've got a whole pile of questions I need help with, but I have restricted access to the internet at the moment, so I mightn't be able to check back here for a little while. Lets hope you guys can help me out.
I know this is a lot to ask, so I wouldn't expect one person to go through and answer every question (although that would be cool). But if everyone can work together to wade through the torrent of questions it'd be greatly appreciated.
- If a the displacement of a particle moving in simple harmonic motion is given by x = 5cos3t + 2sin3t, find the maximum speed of the particle.
- A particle is moving in simple harmonic motion with acceleration d2x/dt2 = -4xms-1. If the particle starts at the origin with a velocity of 3ms-1, find; a) The endpoints of its motion, b) The exact speed when the particle is 1m from the origin.
- A weight is suspended from a spring and pulled down to its maximum displacement of 9cm, and then let go. Its acceleration is given by a = -1/9cm-2. Find; a) The equation of its velocity in terms of x, b) Its exact position when its velocity is 2cms-1
- The period of a particle moving in SHM is 8cm. Calculate its velocity and acceleration (correct to 1 decimal place) when the displacement is 5cm from the center of motion.
- A particle moves in a straight line so that its acceleration at any time is given by d2x/dt2 = -9x. Find its period, amplitude and displacement at time t if initially the particle is 2cm from the origin and has velocity √3cm-1.
- A particle moves in a line so that its acceleration is given by d2x/dt2 = 8 - 2x. Initially, the particle is at the origin and has velocity 3√2ms-1; a) Find the interval in which the particle will travel, b) Is the motion of the particle in simple harmonic motion?
[*]A weight is oscillating at the end of a spring, with velocity given by v2 = 900 - 1600x2cmw-1; a) Find the acceleration of the weight with respect to x, b) Find the period of the motion, c) Find the maximum velocity of the weight.
[*]a) If x = a sin nt + b cos nt, find the acceleration of the particle in terms of t, and show that acceleration = -n2x, b) Find the amplitude and period of the motion, c) Find the maximum velocity.
[*]A particle moves in simple harmonic motion with amplitude 5cm and period 6 seconds. Find; a) The velocity when the particle is 2.5cm from the center of motion, b) The maximum acceleration.
[*]A missile is launched at an initial trajectory of 68o and a velocity of 1200ms-1. Neglecting air resistance anf the curvature of the earth and taking the acceleration due to gravity as 9.8ms-2, calculate; a) The time taken for its flight (to the nearest minute), b) How far away it will hit its target (to the nearest km).
[*]An arrow is fired at a velocity of 24ms-1 and is aimed at the center of a target 1m high and 35m away. The air resitance is negligable for angles of projection less than 45o. At what angle should the arrow be fired? Use g = 10ms-2.
[*]A gun is aimed at a target on the ground 150m away. If the initial velocity is 125ms-1, find the angles at which the gun could be fired to reach the target (use g = 10ms-2).
I know this is a lot to ask, so I wouldn't expect one person to go through and answer every question (although that would be cool). But if everyone can work together to wade through the torrent of questions it'd be greatly appreciated.
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