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Standard XII

Physics

Phase and the General Equation

A lab assista...

Question

A lab assistant has to write the equation of a spring block system doing SHM. At t = 0 the block is in the condition as shown above.He writes the equation as $x = A s i n (ω t + ϕ)$ . Find the value of $ϕ$ ?

$\frac{Π}{3}$

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$\frac{Π}{4}$

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$\frac{Π}{1}$

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$\frac{Π}{2}$

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Solution

The correct option is B
$\frac{Π}{4}$

The equation writen by the assistant is $x = A s i n (ω t + ϕ)$
From the diagram we see that at t=0 the block was at $\frac{A}{\sqrt{2}}$ away from the mean position.
Let's put t=0 in his equation and x= $\frac{A}{\sqrt{2}}$ and solve.
We get $ϕ = \frac{π}{4}$

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A lab assistant has to write the equation of a spring block system doing SHM. At t = 0 the block is in the condition as shown above.He writes the equation as $x = A s i n (ω t + ϕ)$ . Find the value of $ϕ$ ?

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Q. Using equation

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A lab assistant has to write the equation of a spring block system doing SHM. At t = 0 the block is in the condition as shown above.He writes the equation as x=A sin(ω t+ϕ). Find the value of ϕ?

The correct option is B Π4 The equation writen by the assistant is x=A sin(ω t+ϕ) From the diagram we see that at t=0 the block was at A√2away from the mean position. Let's put t=0 in his equation and x= A√2 and solve. We get ϕ=π4

A lab assistant has to write the equation of a spring block system doing SHM. At t = 0 the block is in the condition as shown above.He writes the equation as $x = A s i n (ω t + ϕ)$ . Find the value of $ϕ$ ?