EduNinja

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This question is in two parts. Part 1 is about simple harmonic motion (SHM). Part 2 is about gas in an engine.

Part 1 Simple harmonic motion (SHM)
An object is placed on a frictionless surface. The object is attached by a spring fixed at one end and oscillates at the end of the spring with simple harmonic motion (SHM).

The tension F in the spring is given by F=k x where x is the extension of the spring and k is a constant.

(a)

Show that $\omega^{2}=\frac{k}{m}$ .

[ 2 ]

m a=-k x;
$a=-\frac{k}{m} x ;($ condone lack of negative sign )

\left(\omega^{2}=\frac{k}{m}\right)

or
implied use of defining equation for simple harmonic motion $a=-\omega^{2} x$ ;
(so $\omega^{2}=\frac{k}{m}$ )
m a=-k x so $a=-\left(\frac{k}{m}\right) x$ ;

(b)

One cycle of the variation of displacement with time is shown for two separate mass-spring systems, A and B .

[ 2 ]

(i)

Outline how you would use the graph to confirm that A is performing simple harmonic motion.

[ 2 ]

defines simple harmonic motion as acceleration proportional to negative displacement $/ x=x_{0} \sin \omega t$ ;
correct method for showing how graph leads to the definition;

IB Physics HL C 1 2 Shm Defining Equation Topic Practice

Question 1

Question (a)

Question (b)

Question (i)