Question

mateo adds two labels to the venn diagram shown to explain how velocity and acceleration change during simple harmonic motion. label 1: zero at the equilibrium position label 2: increases with increasing net force velocity acceleration x y z where should mateo place the labels? ∘ label 1: z label 2: z ∘ label 1: x label 2: z ∘ label 1: y label 2: y ∘ label 1: z label 2: x

Explanation:

1. For simple harmonic motion (SHM):

• At the equilibrium position, the acceleration is zero (since net force \( F = -kx \), and at \( x = 0 \), \( F = 0 \), so \( a=\frac{F}{m}=0 \)). Velocity is maximum at equilibrium. So "Zero at the equilibrium position" applies to acceleration (region Z, as Z is unique to Acceleration).
• Acceleration in SHM is \( a = -\frac{k}{m}x \), and net force \( F = -kx \), so acceleration increases with increasing net force (since \( a=\frac{F}{m} \)). This also applies to acceleration (region Z).
• Velocity in SHM has maximum at equilibrium and is related to \( v=\pm\omega\sqrt{A^{2}-x^{2}} \), so "Zero at equilibrium" does not apply to velocity's unique region (X), and "increases with net force" does not apply to velocity. Thus both labels apply to the Acceleration - unique region (Z).

Answer:

Label 1: Z
Label 2: Z