A school laboratory pendulum has a string length of

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Oscillations · Oscillations

Problem

1.20\,\text{m}

. The acceleration due to gravity at sea level is

9.80\,\text{m\,s}^{-2}

. The same pendulum is taken to a hill station where

g

9.70\,\text{m\,s}^{-2}

. (i) Calculate the time period

T_{\text{sea}}

of the pendulum at sea level. (ii) Determine its time period

T_{\text{hill}}

on the hill station without making any other change. (iii) While at the hill station the laboratory assistant accidentally shortens the string by

2\%

. Find the new time period

T'_{\text{hill}}

after this alteration. (iv) Compare

T'_{\text{hill}}

with

T_{\text{sea}}

and state whether the pendulum now runs faster or slower than it did at sea level. Support your answer with numerical values.