f' = 1/(2T) = 0.5T
Introduction to Oscillations
The conditions that lead to simple harmonic motion are as follows:
Consider a block of mass m attached to a spring with force constant k, as shown in the figure (Figure 1). The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x=0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations.
Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block.
The time it takes the block to complete one cycle is called the period. Usually, the period is denoted T and is measured in seconds.
The frequency, denoted f, is the number of cycles that are completed per unit of time: f = 1/T. In SI units, f is measured in inverse seconds, or hertz (Hz).
If the period is doubled, the frequency is
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