Thread: Variation - Please Help

The period T of a simple pendulum is the time taken for one complete small oscillation. T varies directly with the square root of its length L. When the length of the pendulum is 98 cm, the period is exactly 2 seconds.

i) What length should the pendulum be if its period is to be halved?

ii) A grandfather clock is regulated by this pendulum. The pendulum is lengthened to 1 m and the clock started at noon. Calculate the actual time, to the nearest second, when the clock first shows 1 o'clock.

For i) I worked out the length as 1/4 and ii) the time is 2:01. My answers dont look right. Could someone please help?

Originally Posted by xwrathbringerx

The period T of a simple pendulum is the time taken for one complete small oscillation. T varies directly with the square root of its length L. When the length of the pendulum is 98 cm, the period is exactly 2 seconds.

i) What length should the pendulum be if its period is to be halved?

ii) A grandfather clock is regulated by this pendulum. The pendulum is lengthened to 1 m and the clock started at noon. Calculate the actual time, to the nearest second, when the clock first shows 1 o'clock.

For i) I worked out the length as 1/4 and ii) the time is 2:01. My answers dont look right. Could someone please help?

As the period varies directly with the square root of its length you have:

T=k\sqrt{L}

for some constant k.

With L in metres, you are told that:

,

so:



Now what is the period when ?

One hour is 1800 swings of a 2 second pendulum, at what time does the 1 metre pendulum complete 1800 swings?

RonL

Ummm is it 37 s past 1 o'clock?

Originally Posted by xwrathbringerx

Ummm is it 37 s past 1 o'clock?

The period of the m pendulum is:

s

The time for swings is:

s

which is:

s

longer than swings of the s pendulum.

So yes, the time rounded to the nearest second is s past o'clock

RonL