SIMPLE HARMONIC MOTION
Graded examples - Cheetham & Folland

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164     A particle moves with simple harmonic motion between two points which are 10cm apart. At the instant when the particle is 2.0 cm from one of these points, its acceleration is 48 cm s^-2 Find (a) its velocity at the same instant, cms^-1  (b) its time period s,   (c) its maximum velocity cms^-1.  

165     A body is moving with simple harmonic motion with time period 10 s. Find its acceleration at a distance of 20 cm from the centre of its motion cms^-2. If the distance between its two extreme positions is 2.0 m, how long does it take to travel 70 cm from one of these positions?   s

166     A body of mass 4.0 g is attracted towards a fixed point by a force which is proportional to the distance of the body from the point. When the body is 5.0 cm from the point, the force is 4.9 x 10^-2 N. Find the period of oscillation of the body.  s

167     A spring is such that a load of 5.0 g produces an extension of I.0cm. A mass of 0.10kg hangs at the end of the spring in equilibrium. It is now pulled down vertically a distance of 6.0 cm and released. Find (a) the period of vibration of the 0.l0 kg masss, (b) the maximum velocity of the masscms^-1 (c) the velocity of the mass when it is 4.0 cm above the equilibrium position. cms^-1 

168     A small piece of metal suspended from a light, spiral spring produces an extension of 7.9 cm. It is then displaced vertically so that it performs simple harmonic vibrations, 100 of which are observed to take 57 s. What value does this experiment give for the acceleration due to gravity?   ms^-2

169      A scale pan of mass 1.0 kg is attached to a spiral spring and causes it to extend 5.0 cm. A mass of 2.0 kg is placed in the pan which is then released. Find (a) how far the pan will descendcm, (b) the tension in the spring when the pan is at its lowest pointN, (c) the period of oscillation of the pan with the 2.0 kg mass in its  

170     A spring stretches 1.0 cm when loaded with 90 g. With only a light pan hanging on the spring, a mass of 75 g is dropped from a height of 10 cm into the pan. Find (a) the resulting extension of the spring,cm (b) the vertical distance between the highest and lowest positions of the oscillating pancm, (c) the period.s  

171   A ‘seconds pendulum’ is one which travels from one extreme position to the other in one second. Find the length of such a pendulum if the acceleration due to gravity is 9.8 m s^-2 m

172   A pendulum has a period of 2.0s  If it was taken to the moon, what would its time period be? (Acceleration due to gravity on the moon is one sixth of the value of that on the earth.)   s

173  A shelf oscillates vertically with simple harmonic motion and its velocity is 5.0 cms^-1 and 3.0 cm s^-1 when its distances from the mean position are 1.0 cm and 2.0 cm respectively. What is its period? s.  If a mass of 30 g rests on the shelf, find the maximum and minimum force it exerts upon the shelf.   max=N,  min=N

174   A small body rests on a horizontal diaphragm which is making vertical simple harmonic vibrations through a distance of 0.40 cm. What is the maximum number of vibrations that can be made per second if the body is not to be thrown off the diaphragm?  

175  20cm³ of water are poured into a glass U-tube of internal radius 7.0 mm. When the column of water in the U-tube is displaced it oscillates with simple harmonic motion. Find the period.   s

176   A test-tube, mass 12 g and external diameter 3.0 cm, is loaded with 6.0 g of lead shot so that it will float vertically in water. If the test-tube is pushed down slightly and then released it oscillates vertically with simple harmonic motion. Find the period.s What would the period be if the test-tube were floating in alcohol of density 0.80 g cm³?  s

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