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Questions and Answers
What is the amplitude of oscillation for the particle described by the equation $x = 3 ext{sin}(20 ext{π}t) + 4 ext{cos}(20 ext{π}t)$?
What is the amplitude of oscillation for the particle described by the equation $x = 3 ext{sin}(20 ext{π}t) + 4 ext{cos}(20 ext{π}t)$?
Which term in the equation $x = 3 ext{sin}(20 ext{π}t) + 4 ext{cos}(20 ext{π}t)$ represents the oscillating motion?
Which term in the equation $x = 3 ext{sin}(20 ext{π}t) + 4 ext{cos}(20 ext{π}t)$ represents the oscillating motion?
In the equation $x = 3 ext{sin}(20 ext{π}t) + 4 ext{cos}(20 ext{π}t)$, what do the coefficients 3 and 4 represent?
In the equation $x = 3 ext{sin}(20 ext{π}t) + 4 ext{cos}(20 ext{π}t)$, what do the coefficients 3 and 4 represent?
If the value of $t$ changes in the equation $x = 3 ext{sin}(20 ext{π}t) + 4 ext{cos}(20 ext{π}t)$, what will happen to the displacement $x$?
If the value of $t$ changes in the equation $x = 3 ext{sin}(20 ext{π}t) + 4 ext{cos}(20 ext{π}t)$, what will happen to the displacement $x$?
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What happens to the displacement of the particle when $t = 0$ in the equation $x = 3 ext{sin}(20 ext{π}t) + 4 ext{cos}(20 ext{π}t)$?
What happens to the displacement of the particle when $t = 0$ in the equation $x = 3 ext{sin}(20 ext{π}t) + 4 ext{cos}(20 ext{π}t)$?
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Study Notes
Simple Harmonic Motion (SHM)
- Displacement in SHM can be described by a combination of sine and cosine functions.
- The amplitude of oscillation represents the maximum displacement from the equilibrium position.
- To find the amplitude, we need to analyze the trigonometric functions in the displacement equation.
- The formula for amplitude in a simple harmonic motion equation of the form x = A sin(ωt) + B cos(ωt) is: Amplitude = √(A^2 + B^2)
Example 1:
- In the given SHM equation, x = 3sin(20πt) + 4cos(20πt) cm
- A = 3 and B = 4
- Therefore, the amplitude of oscillation is √(3^2 + 4^2) = 5 cm.
- The correct answer is (c).
Example 2:
- The question does not provide the full equation for the particle's motion, making it impossible to analyze and determine the relevant information.
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Description
This quiz focuses on the concepts of Simple Harmonic Motion (SHM), specifically the calculation of amplitude using trigonometric functions. Through examples and equations, participants will explore how to determine the maximum displacement from the equilibrium position. Test your understanding of SHM and improve your skills in analyzing displacement equations!
