Any city incorporated as a city under the council form of government may change its organization thereunder and adopt the modern council form of government. The proceeding to change shall be initiated by a petition asking for such change signed by not less than one-third of the qualified electors of the city. For the purpose of this section, the term “qualified electors of the city” means the total number of qualified electors voting at the preceding general election of the city. The signatures to such petition need not be contained in a single paper, but one of the signers upon each paper shall make oath before an officer competent to administer oaths that each signature appearing upon such paper is the genuine signature of the person whose name it purports to be. Each petition, in addition to the names of the signers, shall contain the address of each petitioner, and the length of the petitioner’s residence in the city. Any petitioner shall be permitted to withdraw that petitioner’s name from a petition within five days after the petition is filed.