A student performs an experiment with a spring‑block simple harmonic oscillator. In the first trial, the amplitude of the oscillations is $3.0\ \mathrm{cm}$, while in the second trial (using the same spring and block), the amplitude of the oscillations is $6.0\ \mathrm{cm}$.
Compare the values of the period, frequency, and maximum speed of the block between these two trials.
The period and frequency will have the same values in the second trial as they had in the first.
$v_{\mathrm{max}}$ will be twice as great in the second trial than in the first.
If the system exhibits simple harmonic motion, then the period and frequency are independent of amplitude. This is because the same spring and block were used in the two trials, so the period and frequency will have the same values in the second trial as they had in the first. But the maximum speed of the block will be greater in the second trial than in the first. Since the amplitude is greater in the second trial, the system possesses more total energy $(E=\displaystyle \frac{1}{2}kA^2)$. So when the block is passing through equilibrium (its position of greatest speed), the second system has more energy to convert to kinetic, meaning that the block will have a greater speed. In fact, from Example 2, we know that $v_{\mathrm{max}}=A\sqrt{\displaystyle \frac{k}{m}}$ so, since $A$ is twice as great in the second trial than in the first, $v_{\mathrm{max}}$ will be twice as great in the second trial than in the first.