Mechanics | Relativity Answers

A sinusoidal wave is described by y (x, t) = 3.0 sin (3.52t 2.01x) cm x is the position along the wave propagation. Determine the amplitude, wave number, wavelength, frequency and velocity of the wave.

The oscillations of two points x1 and x2 at x = 0 and x = 1 m respectively are modelled as follows: y1 = 0.3 sin 4πt and y2 = 0.3 sin (4πt +π / 8) Calculate the wavelength and speed of the associated wave.

Establish the equation of motion of a weakly damped forced oscillator explaining the significance of each term. Differentiate between transient and steady state of the oscillator.

For a damped harmonic oscillator, the equation of motion is m(d^2x/dt^2)+Gama(DX/DT)+kx=0 with m = 0.50 kg, g = 0.70 kgs1 and k = 70 Nm1. Calculate (i) the period of motion, (ii) number of oscillations in which its amplitude will become half of its initial value, (iii) the number of oscillations in which its mechanical energy will drop to half of its initial value, (iv) its relaxation time, and (v) quality factor.

Two collinear harmonic oscillations x1 = 8 sin (100 πt) and x2 = 12 sin (96 πt) are superposed. Calculate the values of time when the amplitude of the resultant oscillation will be (i) maximum and (ii) minimum

The time period of a simple pendulum, called ‘seconds pendulum’, is 2 s. Calculate the length, angular frequency and frequency of the pendulum. What is the difference between a simple pendulum and a compound pendulum?

A simple harmonic motion is represented by x(t)=acos wt Obtain expressions for velocity and acceleration of the oscillator. Also, plot the time variation of displacement, velocity and acceleration of the oscillator.

a toy train of mass 3.0 kg is raveling at 1.5 m/s to the right. the train collides with a similar train and the trains lock together. what was the velocity of the two trains together?

2. A body is projected with a velocity of 20 m/s in a direction making an angle 60° with the horizontal. CCalculate (i) position after 0.5 seconds and (ii) velocity after 0.5 seconds

3. The maximum vertical height of a projectile is 10 m. If the magnitude of the initial velocity is 28 m/s, what is the direction of the initial velocity? (g=9.8 m/s2 )

4. A bullet fired from a gun with a velocity of 140 m/s strikes the ground at the same level as the gun at a distance of 1 km. Find the angle of inclination with the horizontal at which the bullet is fired. (g=9.8 m/s2 )

5.A bullet is fired at an angle of 15° with the horizontal and hits the ground 6 km away. Is it possible to hit a target 10 km away by adjusting the angle of projection assuming the initial speed to be the same?

A box of mass 50 kg is placed on an inclined plane. When the angle of the plane is
increased to 30º, the box begins to slide downwards. Calculate the coefficient of static
friction between the plane and the box. Draw the free body diagram