LU 10 Simple Harmonic Motion PDF

TUTORIAL PRF1016 PHYSICS LU 10: SIMPLE HARMONIC MOTION 1. Figure 1 shows the graph for a particle in simple harmonic motion (SHM). y (cm) 4 0.6 1.2...

TUTORIAL PRF1016 PHYSICS LU 10: SIMPLE HARMONIC MOTION 1. Figure 1 shows the graph for a particle in simple harmonic motion (SHM). y (cm) 4 0.6 1.2 t (s) -4 Figure 1 (a) Determine (i) the amplitude. (ii) the period. (iii) the frequency. (b) Write the displacement equation in the form of y  y o cos (t   ). (c) Determine the velocity and acceleration equation of the particle. Answer: 0.04, 1.2, 0.83 2. The equation of a particle that is performing SHM is given by x  10 sin t , where x in meter and t in second. If the period of the oscillation is 30 s, determine (a) the amplitude. (b) the maximum velocity of the particle (c) the maximum acceleration of the particle. (d) the displacement, velocity and acceleration of the particle when t = 15 s. 𝟐 𝟐 𝟐 𝟐 Answer: 𝟏𝟎, 𝝅, 𝝅 , 𝟎, − 𝝅, , 𝟎 𝟑 𝟒𝟓 𝟑  TUTORIAL PRF1016 PHYSICS 3. Write down an expression (sine function) for the displacement of the motion if the particle is +1.0 cm from the equilibrium position at t = 0 s. A particle undergoes SHM on a straight line with amplitude 3.0 cm and frequency 5.0 Hz. Assume that displacement to the right side of the equilibrium position is positive. 4. The displacement x of an object that undergoing linear SHM is given by the expression below: x  3.5sin  8 t  0.25  where x and t are measured in cm and second respectively. Determine (a) the amplitude, frequency and period of the oscillation. (b) the phase at t = 0.02 s and t = 1.2 s. (c) the displacements at the instants mentioned above. Answer: 𝟑. 𝟓, 𝟒, 𝟎. 𝟐𝟓, 𝟎. 𝟒𝟏𝝅, 𝟗. 𝟖𝟓𝝅, 𝟑. 𝟑𝟔, −𝟏. 𝟓𝟗 5. (a) Prove that the acceleration of SHM is a   2 x from the equation of x  A sin t (b) Prove that v   A  x 2 2 by using the relationship between velocity, v and displacement, x. 6. Figure 2 shows the graph of the forces acting on a particle of mass 2 kg. Determine F (N) 20 x (m) - 0.1 0.1 - 20 Figure 2 (a) the amplitude. (b) the angular frequency, period, and maximum velocity of the particle. Answer: 𝟎. 𝟏, 𝟏𝟎, 𝟎. 𝟔𝟑, 𝟏  TUTORIAL PRF1016 PHYSICS 7. The motion of an object that undergoes simple harmonic motion begins at its equilibrium position. It completes 20 cycles in 5 seconds with an amplitude of 9 cm. (a) Write an equation of displacement in terms of time. (b) Sketch a graph that shows the displacement as a function of time. 8. (a) The displacement of a particle undergoing simple harmonic motion is described as equation below 𝑥 = 15 sin(14𝜋𝑡 + 2𝜋) where the amplitude is in cm, time is in s and phase constant is in rad. Determine (i) the displacement when 𝑡 = 0.6 s (ii) the velocity when 𝑡 = 0.6 s. (iii) the acceleration when 𝑡 = 0.6 s. Answer: 14.26, 2.03, –275.96 (b) Figure 3 shows a graph of the potential energy, U with displacement x from equilibrium for a 3 kg object that performs simple harmonic motion. Determine the force on the object when 𝑥 = 0.2 m. U(J) 14 x (m) −0.4 0.4 Figure 3 Answer: – 34.93  TUTORIAL PRF1016 PHYSICS 9. A 300 g mass vibrates according to the equation 𝑥 = 0.38 sin(6.50𝑡), where x is in meters and t is in seconds. (a) Calculate the frequency. (b) Calculate the total energy. (c) Calculate the kinetic energy and potential energy when 𝑥 = 9.0 𝑐𝑚. (d) Sketch the graph of x vs t showing the correct amplitude and period. Answer: 1.034, 0.92, 0.051, 0.86 10. The motion of a particle that undergoes simple harmonic motion begins at its maximum displacement of +20 cm. Its motion repeats every 4.0 s. (a) Determine the amplitude of the motion. (b) Calculate the frequency of the motion. (c) Determine the angular velocity of the motion. (d) Write an equation to describe the motion of the particle. (e) Calculate its maximum velocity. (f) Sketch a graph that shows the acceleration as a function of time. (g) Determine the position of the particle at 𝑡 = 50 𝑚𝑠. Answer: 0.2, 0.25, 1.57, 0.314, 0.19