Download App

PART - 2 CH - 13 Oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 13 Oscillations3 Marks
Question
If a mass of 0.8 kg is moving in simple harmonic motion starting from equilibrium position. The dimensions of the body of mass 1.0 m and if the period is 11/7 sec then 0.6 m. Find velocity of the particle at displacement and also write the equation of motion.
✓

Answer

Given :
$\begin{array}{l}m=0.8 kg \\A=1.0 m\end{array}$
Period $\quad T=\frac{11}{7} sec \therefore$ Frequency $(n)=\frac{7}{11}$ per sec.
$ \begin{aligned}\text {Displacement}\quad(x) & =0.6 m \\v & =?\end{aligned}$
Equation of the motion $=$ ?
between velocity (v) and displacement ( x ) in simple harmonic motion, their relation :
$\begin{aligned}v & =\omega \sqrt{A^2-x^2}\ldots\ldots (1) \\\omega & =2 \pi n \\& =2 \times \frac{22}{7} \times \frac{7}{11}=4 \text { radians } / sec\end{aligned}$
Putting the value of $v$ in equation (1)
$\begin{aligned}v & =4 \sqrt{(1)^2-(0.6)^2} \\& =4 \sqrt{1-0.36}=4 \sqrt{0.64} \\& =4 \times 0.8=3.2 m / s\end{aligned}$
$\begin{aligned}\text { Displacement } y & =A \sin \omega t \\& =1.0 \sin (4 t) \because \omega=4 \text { radian } / sec \\y & =1.0 \sin (4 t) m\end{aligned}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from PART - 2 CH - 13 Oscillations→PART - 2 CH - 13 Oscillations — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Weights of $50g$ and $40g$ are connected by a stringpassing over a smooth pulley. If the system travels $2.18m$ in the first $2$ seconds, find the value of g.
→
Given a + b + c + d = 0, which of the following statements are correct: The magnitude of (a + c) equals the magnitude of ( b + d).
→
The displacement vector of a particle of mass m is given by $\text{r}\text{(t})=\hat{\text{i}}\text{A}\cos\omega\text{t}+\hat{\text{j}}\text{B}\sin\omega\text{t}.$Show that the trajectory is an ellipse.
→
The number of particles crossing per unit area perpendicular to x-axis in unit time N is given by: $\text{N}=-\text{D}\Big(\frac{\text{n}_2-\text{n}_1}{\text{x}_2-\text{x}_1}\Big),$ where $n_1$ and $n_2$ are the number of particles per unit volume at $x_1$ and $x_2$ respectively. Deduce the dimensional formula for D.
→
Suppose white light falls on a double slit but one slit is covered by a violet filter (allowing $\lambda=400\text{nm}$). Describe the nature of the fringe pattern observed.
→
Consider a Carnot's cycle operating between $T_1=500 K$ and $T_2=300 K$ producing 1 kJ of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs.
→
A person looks at different trees in an open space with the following details. Arrange the trees in decreasing order of their apparent sizes.
Tree Height(m) Distance form the eye(m)
A 2.8 50
B 2.5 80
C 1.8 70
D 2.8 100
→
Three particles, each of mass $200g$, are kept at the corners of an equilateral triangle of side $10\ cm$. Find the moment of inertia of the system about an axis:
  1. Joining two of the particles.
  2. Passing through one of the particles and perpendicular to the plane of the particles.
→
Find the potential energy of a system of four particles placed at the vertices of a square of side $l$. Also obtain the potential at the centre of the square.
→
A balloon is filled with water. To what depth should it to be taken into a lake so that its volume decreases by $0.01 \%$ whereas Bulk Modulus of elasticity of water is $2 \times 10^9 N / m ^2$.
→