## Related questions with answers

The disk rotates in the horizontal plane with constant angular velocity $\Omega=12 \mathrm{rad} / \mathrm{s}$. The mass $m=2 \mathrm{~kg}$ slides in a smooth slot in the disk and is attached to a spring with constant $k=860 \mathrm{~N} / \mathrm{m}$. The radial position of the mass when the spring is unstretched is $r=0.2 \mathrm{~m}$. At $t=0$, the mass is in the position $r=0.4 \mathrm{~m}$ and $d r / d t=0$. Determine the position $r$ as a function of time.

Solution

Verified**Given:**
Angular velocity: $12\ \text{rad/s}$
Mass of the slider: $2\ \text{kg}$
Spring constant: $860\ \text{N/m}$
Position of the mass when spring is unstretched: $0.20\ \text{m}$
Position at time, t=0 and $\text{dr}/\text{dt}=0$: $0.40\ \text{m}$

**We are required:**
To determine the position as a function of time.

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