Physics 1B03summer - Lecture 7 HOMEWORK QUESTION Please do this question and hand it by Tuesday after the reading week, in class: A 50kg child slides down a 45 o frictionless hill for 60m, starting with an initial velocity of 2m/s. The child then slides for 10m over a flat surface that has a coefficient of kinetic friction of 0.15, and finally back up another frictionless hill with a slope of 30 o. Draw a pictures of the problem and determine how far on the 2 nd hill the child ends up (not the height).

Physics 1B03summer - Lecture 7 Oscillatory Motion (Chapter 14) Kinematics of Simple Harmonic Motion Mass on a spring Energy Knight sections

Physics 1B03summer - Lecture 7 We have examined the kinematics of linear motion with uniform acceleration. There are other simple types of motion. Many phenomena are repetitive or oscillatory. Example: Block and spring, pendulum, vibrations (musical instruments, molecules) M Oscillatory Motion

Physics 1B03summer - Lecture 7 Spring and mass M Equilibrium: no net force M The spring force is always directed back towards equilibrium. This leads to an oscillation of the block about the equilibrium position. M For an ideal spring, the force is proportional to displacement. For this particular force behaviour, the oscillation is simple harmonic motion. x F = -kx

Physics 1B03summer - Lecture 7 SHM: x(t)x(t) t A -A T A = amplitude  = phase constant  = angular frequency A is the maximum value of x (x ranges from +A to -A).  gives the initial position at t=0: x(0) = A cos .  is related to the period T and the frequency f = 1/T T (period) is the time for one complete cycle (seconds). Frequency f (cycles per second or hertz, Hz) is the number of complete cycles per unit time.

Physics 1B03summer - Lecture 7 Three constants specify the motion: Amplitude, A Angular Frequency,  Initial phase (or phase constant),  In general: t x(t)x(t) Φ These graphs are a mathematical representation of motion as a function of time, now how the object actually moves – notice the axes. x(t) is simply the displacement from some position.

Physics 1B03summer - Lecture 7 The quantity (  t +  ) is called the phase, and is measured in radians. The cosine function traces out one complete cycle when the phase changes by 2  radians. The phase is not a physical angle! The period T of the motion is the time needed to repeat the cycle: units: radians/second or s -1

Physics 1B03summer - Lecture 7 Example The block is at its equilibrium position and is set in motion by hitting it (and giving it an initial velocity) at time t = 0. Its motion is SHM with amplitude 5 cm and period 2 seconds. Write the function x(t). M x v0v0

Physics 1B03summer - Lecture 7 QUIZ The block is at x 0 = +5 cm, with positive velocity v 0, at time t = 0. Its motion is SHM with amplitude 10 cm and period 2 seconds. If x(t) = A cos (  t   ), the phase constant  should be: M x0x0 v0v0 A)0 o B)30 o C)60 o D)-30 o E)-60 o