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0.22 m/s is the speed when the displacement is 1.75 cm.
Given:
A simple harmonic oscillator has;
Amplitude (A) =3.50 cm = 0.035 m
Maximum Speed (Vmax) = 26.0 cm/s = 0.26 m/s
Displacment (d) = 1.75cm =0.0175 m
The displacement d, whose maximum is the amplitude A , is expressed as:
∴ d = A Sin wt
= Sin wt
t = Sin⁻¹ (
)
v = - Aw cos wt
v = - Aw cos w [ sin⁻¹ (
) ]
v = - Aw cos [ sin⁻¹ () ]
Speed, v = Vmax cos [ sin⁻¹ () ] ∵ Vmax = Aw
v = 0.26 cos [ sin⁻¹ ( ) ]
v = 0.22 m/s
Therefore, 0.22 m/s is the speed when the displacement is 1.75 cm.
Learn more about simple harmonic motion here:
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