To determine the maximum displacement from the equilibrium position in simple harmonic motion described by the equation [tex]\( d = 8 \sin(47) \)[/tex], we need to understand the components of the equation.
In the equation [tex]\( d = 8 \sin(47) \)[/tex]:
- [tex]\( d \)[/tex] represents the displacement.
- The coefficient 8 is known as the amplitude.
- The term [tex]\( \sin(47) \)[/tex] indicates the sine function at an angle or a phase, which oscillates between -1 and 1.
The maximum displacement in simple harmonic motion occurs when the sine function reaches its peak value. The sine function attains its maximum value of 1. Therefore, the expression for the displacement [tex]\( d \)[/tex] reaches its highest value when [tex]\( \sin(47) = 1 \)[/tex].
Substituting [tex]\( \sin(47) = 1 \)[/tex] into the equation, we get:
[tex]\[ d_{\text{max}} = 8 \times 1 \][/tex]
Hence, the maximum displacement from the equilibrium position is:
[tex]\[ d_{\text{max}} = 8 \][/tex]
So, the maximum displacement from the equilibrium position is [tex]\( 8 \)[/tex] units.
