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D roblems For Practice q, , 1, Asimple harmonic oscillation is represented by the, equation, y= 0.40sin (440 + 0.61), Here y and f are in m and s respectively. What are, the values of (i) amplitude (ii) angular frequency, (iii) frequency of oscillations (iv) time period of, oscillations and (v) initial phase ?, [Ans. (i) 0.40 m (ii) 440 rad s”! (iii) 70 Hz, (iv) 0.0143 s (v) 0.61 rad], 2. The periodic time of a body executing SHM is 2 s., After how much time interval from ¢ = 0, will its, displacement be half of its amplitude ?, , : (Ans. 1/6s), , 3. A particle executes SHM represented by the, , equation : 10y = 0.1sin 50 x t, where the displacement, , y is in metre and time ft in second. Find the, amplitude and frequency of the particle., , (Ans. A=0.01m, v = 25 Hz), , 4, The displacement: of a particle executing periodic, , motion is given by y=4 cos? (t / 2) sin (1000 t). Find, , the independent constituent SHM’s. [IT 93], , [Ans. sin (10016), sin (1000 t), sin (999¢ )}, , 5. A particle executing SHM completes 1200 oscilla, tions per minute and passes through the mean, , position with a velocity of 31.4 ms” !. Determine the