CHapter11 Section 2 solving simple harmonics

Objectives  Identify the amplitude of vibration.  Recognize the relationship between period and frequency.  Calculate the period and frequency of an object vibrating with simple harmonic motion.

Amplitude  In the absence of friction, a moving trapeze always returns to the same maximum displacement after each swing.  The amplitude is the maximum displacement from equilibrium.

Periods and frequencies  The period (T) is the time (in seconds) it takes for one complete cycle of the motion.  The SI unit of period is seconds (s).  The frequency ( f ) is the number of complete cycles that occur in one second.  The SI unit of frequency is s-1, which is called a hertz (Hz).

Periods and frequencies  Period and frequency are inversely related: Since frequency is cycles per second and since period is seconds per cycle, frequency and period are reciprocals of each other:

Measuring of simple harmonics

Period of a simple pendulum  The period of a simple pendulum depends on the length and on the free- fall acceleration. The period does not depend on the mass of the bob or on the amplitude (for small angles).

Example 1  An orangutan on a swing swings in simple harmonic motion with a period of 4.2 s. Calculate the length of the cables supporting the swing.

Example 2  You need to know the height of a tower  But darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 12s. How tall is the tower.

Student guided practice  Do problems 1-3 in your book page 375.

Period of mass system  The period of an ideal mass-spring system depends on the mass and on the spring constant. The period does not depend on the amplitude. This equation applies only for systems in which the spring obeys Hooke’s law.

Example  The body of a 1275kg car is supported on a frame by four springs. Two people riding in the car have a combined mass of 153kg. When driven over a pothole in the road the frame vibrates with a period of 0.840s. Find the spring constant of a single spring.

Student guided practice  Do problems 1-2 in your book page 377.

homework  Do worksheet problems 1-5

closure  Today we learned about period and frequency  Next we are going to learn about waves