Question

A particle executing SHM having amplitude 10cm and time period 8 sec, what is displacement of particle after 4 sec;
A. 5cm
B. -20cm
C. 10cm
D. -5cm
E. -10cm​

Answer 1

${ \boxed{\boxed{\begin{array}{cc} \bf \: given \\ \\ \rm \to \: amplitude \: \: A = 10 \: cm\:=\:\frac{10}{100}\:m \\ \rm \to \: period \: \: T = 8 \: s \\ \rm \to \: time \: \: t = 4 \: s \\ \\ \rm \to \: displacement \: \: s = \: to \: find \\ \\ \pink{ \bf \: we \: know \:that \: , }\\ \\ \rm \: x = A \: cos \: \omega \: t \\ \\ \rm \: = A \: cos \: \frac{2\pi}{T} \times t \\ \\ = \frac{10}{100} \times cos \frac{2\pi}{8} \times 4 \\ \\ = \frac{10}{100} \times cos\pi \\ \\ = \frac{10}{100} \times ( - 1) \\ \\ = - 0.1 \: m \\ \\ = - 10 \: cm \\ \\ \pink{ \boxed{\boxed{\begin{array}{cc} \therefore \: \rm \: displacement \: \: \: x = - 10 \: cm \end{array}}}}\end{array}}}}$