For Equation$\mathbf{\text{x}}\mathbf{=}{\mathbf{\text{x}}}_{\mathbf{m}}\mathbf{}\mathbf{\text{cos}}\mathbf{(}\mathbf{\omega }\mathbf{\text{t}}\mathbf{+}\mathbf{\varphi }\mathbf{)}$, suppose the amplitude${\text{x}}_{\text{m}}$is given by

${\mathbf{\text{x}}}_{\mathbf{m}}\mathbf{=}\frac{{\mathbf{\text{F}}}_{\mathbf{\text{m}}}}{{\mathbf{[}{\mathbf{\text{m}}}^{\mathbf{2}}{\mathbf{(}{\mathbf{\omega }}_{\mathbf{d}}^{\mathbf{2}}\mathbf{-}{\mathbf{\omega }}^{\mathbf{2}}\mathbf{)}}^{\mathbf{2}}\mathbf{+}{\mathbf{b}}^{\mathbf{2}}{\mathbf{\omega }}_{\mathbf{d}}^{\mathbf{2}}\mathbf{]}}^{\mathbf{1}\mathbf{/}\mathbf{2}}}$

where${\mathbf{\text{F}}}_{\mathbf{m}}$is the (constant) amplitude of the external oscillating force exerted on the spring by the rigid support in Figure below. At resonance,

1. what is the amplitude of the oscillating object?
2. what is the velocity amplitude of the oscillating object?

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