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SHM – Derivation of equation

SHM or SHMSimple Harmonic Motion is the fundamental concept to various complex systems. The following links will give you the opportunity to understand the concept well.

  1. http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html
  2. http://www.splung.com/content/sid/2/page/shm
  3. http://en.wikipedia.org/wiki/Simple_harmonic_motion


For a circular motion centripetal force is required. Is there any other force which could replace centripetal force to obtain a circular motion? (Asked Sajin)


centripetal forcePlease note that Centripetal Force is the net force that must be acting towards the centre of the circular path. It may be provided by one or more of the forces of different kinds. It is not a kind of force like the frictional force or gravitational force. In different cases the centripetal force is provided by different forces.

For example, when we whirl a stone tied to the end of a rope in a horizontal plane, the tension in the string provides the centripetal force. Here the real force acting is the tension in the string and its magnitude equals the centripetal force mv^2/r.

Read more at the following links

  1. http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html
  2. http://en.wikipedia.org/wiki/Centripetal_force
  3. http://www.physicsclassroom.com/Class/circles/u6l1c.cfm

A few numerical problems from laws of motion

  1. A worker pulls a 200. N packing crate with an applied force of 55.0 N.  The crate accelerates at a rate of 0.250  m/s(squared).  What is the coefficient of kinetic friction between the crate and the factory floor?
  2. A student pulls a 150. N sled up a 28 degree slope at a constant speed by applying a force of 100. N.  Near the top of the hill he releases the sled.  With what acceleration does the sled go down the hill?
  3. A 200. N crate rests on a ramp; the maximum angle just before it slips is 25 degrees with the horizontal.  What is the coefficient of static friction between the crate and the surface of the ramp?
  4. A man pulls a sled with a weight of 200. N with a constant velocity across a horizontal snow surface.  If a force of 80N is being applied to the sled rope at an angle of 53 degrees to the ground, what is the coefficient of friction between the sled and the ground?
  5. A jet plane is flying with  a constant speed along a straight line at an angle of 30degree  above the horizontal. The weight of plane is 86 500N. Its engine provides a forward thrust T of 103 000N. The lift of force L(directed perpendicular to the wings)and the force R of air resistance (directed opposite to the motion)act on the plane. Find L & R

How is the equation of simple harmonic motion y=a sinwt derived and what is the physical meaning of phase?

How is the equation of simple harmonic motion y=a sinwt derived and what is the physical meaning of phase?

Terminal Speed and Newton’s Laws of motion

What is terminal speed? When a skydiver has reached terminal speed, what is the air resistance equal to? What is the skydivers acceleration?

Heating up of water due to shaking

Would shaking a bottle of chilled water, cause it to warm up, even slightly, due to some kind of friction?


Shaking BottleYes, This is due to friction (Viscous forces). The different layers of water resist relative motion and the work done in producing motion against the viscous force appears  as heat.

Numerical from Motion and Force for CBSE Class 9 SA1

A steam engine of mass 30000 kg pulls 2 wagons each of mass 20000 kg with an acceleration of 0.2 m/s/s. neglecting frictional force calculate (i) the force exerted by the engine (ii) the force experienced by each wagon

(Srija posted)


In this case the engine is pulling the rest of the wagons.

The force exerted by the engine = total mass of the wagons x acceleration = 2 x 20000 x 0.2 = 8000 N

Each wagon experiences a net force = 20000 x 0.2 = 4000 N

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