A group of mechanical engineers conducted an experiment to evaluate how the frequency of a… — ACT

A group of mechanical engineers conducted an experiment to evaluate how the frequency of ambient mechanical vibration affects the peak electrical voltage output of a piezoelectric cantilever beam. In each trial, a cantilever beam of identical length ( $10\text{ cm}$ ), thickness ( $1\text{ mm}$ ), and material composition (lead zirconate titanate) was mounted on a shaker table maintained at a constant displacement amplitude of $0.5\text{ mm}$ and a room temperature of $22^\circ\text{C}$ . The vibration frequency was varied across $\text{50 Hz}$ , $\text{100 Hz}$ , $\text{150 Hz}$ , and $\text{200 Hz}$ , and the peak output voltage generated across a $100\text{ }\Omega$ load resistor was recorded.

Match each experimental component listed on the left with its corresponding variable classification on the right.

Vibration frequency of the shaker table ( $\text{50--200 Hz}$ )Independent Variable
Peak electrical voltage output measured across the load resistorDependent Variable
Shaker table displacement amplitude ( $0.5\text{ mm}$ )Controlled Variable

Answer

The vibration frequency is the independent variable, the peak voltage output is the dependent variable, and the shaker table displacement amplitude is a controlled variable.

The vibration frequency is manipulated by the experimenter, making it the independent variable. The peak electrical voltage output is the measured response to these changes, making it the dependent variable. The shaker table displacement amplitude is kept constant at 0.5 mm to prevent confounded results, making it a controlled variable.

Step-by-Step Solution

Identify the condition or factor systematically manipulated by the researchers.

The vibration frequency of the shaker table was changed across trials (50 Hz, 100 Hz, 150 Hz, 200 Hz), identifying it as the independent variable.

The independent variable is the factor intentionally varied by the experimenter to test its effect.

Identify the factor measured to determine the outcome of the manipulation.

The peak electrical voltage output generated across the resistor was measured, identifying it as the dependent variable.

The dependent variable is the response being measured that changes depending on the independent variable.

Identify the parameters held constant throughout all experimental trials.

The shaker table displacement amplitude (0.5 mm), beam dimensions, material, and temperature were kept constant, identifying them as controlled variables.

Controlled variables are kept constant to ensure that any observed changes in the dependent variable are solely attributable to the independent variable.

Key Concept

Distinguishing between independent, dependent, and controlled variables in an experimental setup.

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