Advertisements
Advertisements
प्रश्न
The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed?
Advertisements
उत्तर १
Stroke of piston = 2 times the amplitude
Let A = amplitude,stroke = 1 m
`:. => A = 1/2 m`
Angular frequency, ` omega = 200 "rad/min"`
`V_"max" = ?`
We know that the maximum speed of the block when the amplitude is A
`V_"max" = omegaA = 200 xx 1/2 = 100 "m.min"`
`= 100/60 = 5/3 ms6(-1)= 1.67 ms^(-1)`
उत्तर २
Angular frequency of the piston, ω = 200 rad/ min.
Stroke = 1.0 m
Amplitude, `A = 1.0/ 2= 0.5 m`
The maximum speed (vmax) of the piston is give by the relation:
`V_"max" = Aomega`
`= 200 xx 0.5 = 100 "m/min"`
संबंधित प्रश्न
The periodic time of a linear harmonic oscillator is 2π second, with maximum displacement of 1 cm. If the particle starts from extreme position, find the displacement of the particle after π/3 seconds.
The total mechanical energy of a spring-mass system in simple harmonic motion is \[E = \frac{1}{2}m \omega^2 A^2 .\] Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will
A particle moves in a circular path with a uniform speed. Its motion is
A small block of mass m is kept on a bigger block of mass M which is attached to a vertical spring of spring constant k as shown in the figure. The system oscillates vertically. (a) Find the resultant force on the smaller block when it is displaced through a distance x above its equilibrium position. (b) Find the normal force on the smaller block at this position. When is this force smallest in magnitude? (c) What can be the maximum amplitude with which the two blocks may oscillate together?
The string the spring and the pulley shown in figure are light. Find the time period of the mass m.
Find the time period of small oscillations of the following systems. (a) A metre stick suspended through the 20 cm mark. (b) A ring of mass m and radius r suspended through a point on its periphery. (c) A uniform square plate of edge a suspended through a corner. (d) A uniform disc of mass m and radius r suspended through a point r/2 away from the centre.
A uniform disc of radius r is to be suspended through a small hole made in the disc. Find the minimum possible time period of the disc for small oscillations. What should be the distance of the hole from the centre for it to have minimum time period?
A body of mass 1 kg is mafe to oscillate on a spring of force constant 16 N/m. Calculate (a) Angular frequency, (b) Frequency of vibrations.
The period of oscillation of a body of mass m1 suspended from a light spring is T. When a body of mass m2 is tied to the first body and the system is made to oscillate, the period is 2T. Compare the masses m1 and m2
A 20 cm wide thin circular disc of mass 200 g is suspended to rigid support from a thin metallic string. By holding the rim of the disc, the string is twisted through 60° and released. It now performs angular oscillations of period 1 second. Calculate the maximum restoring torque generated in the string under undamped conditions. (π3 ≈ 31)
Find the number of oscillations performed per minute by a magnet is vibrating in the plane of a uniform field of 1.6 × 10-5 Wb/m2. The magnet has a moment of inertia 3 × 10-6 kg/m2 and magnetic moment 3 A m2.
The maximum speed of a particle executing S.H.M. is 10 m/s and maximum acceleration is 31.4 m/s2. Its periodic time is ______
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
The rotation of the earth about its axis.
When two displacements represented by y1 = a sin(ωt) and y2 = b cos(ωt) are superimposed the motion is ______.
The equation of motion of a particle is x = a cos (αt)2. The motion is ______.
What are the two basic characteristics of a simple harmonic motion?
A person normally weighing 50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 2.0 s–1 and an amplitude 5.0 cm. A weighing machine on the platform gives the persons weight against time.
- Will there be any change in weight of the body, during the oscillation?
- If answer to part (a) is yes, what will be the maximum and minimum reading in the machine and at which position?
When a particle executes Simple Harmonic Motion, the nature of the graph of velocity as a function of displacement will be ______.
