The oscillation of a simple harmonic oscillator is described by the equation
where t is expressed in seconds. Determine the amplitude, time-period and frequency of oscillation, maximum velocity, maximum acceleration and initial displacement of the oscillator.
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The distance between the oxygen molecule and each of the hydrogen atoms in a wate molecule is 0.96 Å and the angle between the two oxygen-hydrogen bonds is 105°. Treating the atoms as particles, find the centre of mass of the system.
Obtain the derivative and unit tangent vector at for a vector function
A cylindrical drum has a radius of 0.45 m and is initially at rest. It is then given an angular acceleration of 0.40 rad At time t = 8.0 s calculate (i) the angular speed of the drum, (ii) the centripetal acceleration of a point on the rim of the drum, (iii) the tangential acceleration at that point, and (iv) the resultant acceleration at that point.
The following two orthogonal oscillations act on a body simultaneously:
Determine the path of resultant motion of the body.
Determine the projection of on
where
and
A damped harmonic oscillator has a first amplitude of 30 cm. The amplitude reduces to 3 cm after 100 oscillations. If the period of damping is 9.2s calculate the logarithmic decrement and damping factor. Also determine the number of oscillations in which the amplitude drops by 50 percent.