The displacement of a particle varies according to the relation x = 4(cosπt + sinπt).
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displacement
y=4(cosπt+sinπt)
y=4cosπt+4sinπt
Let
Rcos Φ=4 π
R sinΦ=4
y=R sinΦcosπt+R cosΦsinπt
y=R sin( πt+Φ)
R is the amplitude
squaring and adding the terms
R=root of(4^2+4^2)=4root2 units
Therefore amplitude=4 root 2 units
displacement
y=4(cosπt+sinπt)
y=4cosπt+4sinπt
Let
Rcos Φ=4 π
R sinΦ=4
y=R sinΦcosπt+R cosΦsinπt
y=R sin( πt+Φ)
R is the amplitude
squaring and adding the terms
R=root of(4^2+4^2)=4root2 units
Therefore amplitude=4 root 2 units
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