Question

1. Convert this equation to linear form T=2 π √ h ^2 +k^2 /gh

Answer 1

Consider the equation

$$T=2\pi\sqrt{\frac{h^2+k^2}{gh}}.$$

Divide the part inside the root by gh:

$$T=\frac{2\pi}{\sqrt{g}}\sqrt{h+\frac{k^2}{h}}.$$

Multiply the part inside the root by h:

$$T=\frac{2\pi}{\sqrt{g}}\sqrt{h^2+k^2}.$$

If k<<1, we have

$$T=\frac{2\pi}{\sqrt{g}}\cdot h.$$