Questions: If the plot below represents a simple harmonic oscillator's position versus time, Plot [Select] represents the velocity of the oscillator, and Plot [Select] represents the acceleration of the oscillator.

If the plot below represents a simple harmonic oscillator's position versus time, Plot [Select] represents the velocity of the oscillator, and Plot [Select] represents the acceleration of the oscillator.

Transcript text: If the plot below represents a simple harmonic oscillator's position versus time, Plot [Select] represents the velocity of the oscillator, and Plot [Select] represents the acceleration of the oscillator.

Solution

Solution Steps

Step 1: Find the velocity plot

The velocity is the derivative (rate of change) of the position. The position graph starts at a maximum. The slope at this point is zero. The velocity should thus start at zero. As the position decreases, the velocity becomes negative, reaching a maximum negative value when the position graph crosses zero. Plot A shows this behavior.

Step 2: Find the acceleration plot

The acceleration is the derivative of the velocity. Looking at Plot A (velocity), the velocity starts at zero, has a negative slope initially, reaches a minimum, and then increases. The acceleration graph should therefore start negative, reach a most negative value when the velocity is zero, then become less negative and cross zero when the velocity is at a minimum. It should then continue becoming more and more positive until the velocity is back to zero. This behavior is shown in Plot C.