#### Periodic Motion Short Answer Questions

#### 1. Define second’s pendulum. If it is taken to moon, will it gain or lose time? Why?

**2. The girl on the swing stands up. What will be the effect on the periodic time of the swing?**

**3. If the length of the simple pendulum is increased by 8 times its original length, will its time period change? If yes, by how much?**

**4. A simple harmonic motion is represented by y=acos(ω+φ)in usual notation. Find its acceleration.**

**5. A body is moving in a circular path with constant speed. Is this motion a simple harmonic? Explain.**

**6. Suppose a hole is dug in the earth through its centre. A ball is dropped into the hole. Will the ball return to the thrower? Explain.**

**7. A particle executing simple harmonic motion comes to rest at the extreme positions. Is the resultant force on the particle zero at these positions according to**

**Newton’s first law?**

**8. A small creature moves with constant speed in a vertical circle on a bright**

**day. Does its shadow formed by the sun on a horizontal plane move in a simple harmonic motion?**

**9.what is resonance ?**

### Long Answer Questions

**10. Define SHM. Deduce a relation for the total energy of SHM.**

**11. Define simple pendulum. Show that motion of bob of a simple pendulum is**

**simple harmonic. Obtain an expression for its frequency.**

**12. Show that motion of vertical mass-spring system is simple harmonic and**

**deduce its time period.**

**Numerical Answer Questions
**

**13. A block of mass 5 kg executes simple harmonic motion under the restoring**

**Force of a spring. The amplitude and the time period of the motion are 0.1**

**m and 3.14 s respectively. Find the maximum force exerted by the spring**

**on the block.**

**14. A glider with mass m= 2.00 kg sits on a frictionless horizontal air track,**

**connected to a spring with force constant k = 5.00 N/m. You pull the glider,**

**stretching the spring 0.100 m and then release it with no initial velocity.**

**The crate glider begins to move back towards it equilibrium position (x=0).**

**What is its velocity when x= 0.080 m?**

**15. A simple pendulum has a period of 4.2 second, when the pendulum is shortened by 1**

**m the period is 3.7 second. Find these measurements, calculate the calculate the**

**acceleration of free fall the original length of the pendulum.**

**16. The displacement y of a mass vibrating with simple harmonic motion is**

**given by y= 20sinπt, where y is in millimeter and t is in second. What is:**

**i) amplitude**

**ii) the period**

**iii) the velocity at t=0.**